%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO604+1 : TPTP v9.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:57 AM UTC 2025
% Result : Theorem 18.25s 18.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO604+1 : TPTP v9.0.0. Released v7.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:16:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 18.25/18.41 % SZS status Theorem
% 18.25/18.41 % SZS output start Proof
% 18.25/18.41 tff(g_false_only_type, type, (
% 18.25/18.41 g_false_only: ( $i * $i ) > $o)).
% 18.25/18.41 tff(tptp_fun_B_3_type, type, (
% 18.25/18.41 tptp_fun_B_3: $i > $i)).
% 18.25/18.41 tff(tptp_fun_A_0_type, type, (
% 18.25/18.41 tptp_fun_A_0: $i)).
% 18.25/18.41 tff(tptp_fun_C_4_type, type, (
% 18.25/18.41 tptp_fun_C_4: $i > $i)).
% 18.25/18.41 tff(g_both_type, type, (
% 18.25/18.41 g_both: ( $i * $i ) > $o)).
% 18.25/18.41 tff(g_true_only_type, type, (
% 18.25/18.41 g_true_only: ( $i * $i ) > $o)).
% 18.25/18.41 tff(tptp_fun_C_2_type, type, (
% 18.25/18.41 tptp_fun_C_2: $i > $i)).
% 18.25/18.41 tff(tptp_fun_C_1_type, type, (
% 18.25/18.41 tptp_fun_C_1: $i > $i)).
% 18.25/18.41 tff(tptp_fun_C_5_type, type, (
% 18.25/18.41 tptp_fun_C_5: $i > $i)).
% 18.25/18.41 tff(tptp_fun_A_6_type, type, (
% 18.25/18.41 tptp_fun_A_6: $i)).
% 18.25/18.41 tff(g_true_type, type, (
% 18.25/18.41 g_true: ( $i * $i ) > $o)).
% 18.25/18.41 tff(g_false_type, type, (
% 18.25/18.41 g_false: ( $i * $i ) > $o)).
% 18.25/18.41 tff(1,assumption,(![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C))), introduced(assumption)).
% 18.25/18.41 tff(2,assumption,(~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))), introduced(assumption)).
% 18.25/18.41 tff(3,plain,
% 18.25/18.41 ((g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))) | (~g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))),
% 18.25/18.41 inference(tautology,[status(thm)],[])).
% 18.25/18.41 tff(4,plain,
% 18.25/18.41 (~g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))),
% 18.25/18.41 inference(unit_resolution,[status(thm)],[3, 2])).
% 18.25/18.41 tff(5,plain,
% 18.25/18.41 ((g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))) | (~g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))))),
% 18.25/18.41 inference(tautology,[status(thm)],[])).
% 18.25/18.41 tff(6,plain,
% 18.25/18.41 (~g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0)))),
% 18.25/18.41 inference(unit_resolution,[status(thm)],[5, 2])).
% 18.25/18.41 tff(7,plain,
% 18.25/18.41 (((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C))) | (g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))))) <=> ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C))) | g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))))),
% 18.25/18.41 inference(rewrite,[status(thm)],[])).
% 18.25/18.41 tff(8,plain,
% 18.25/18.41 ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C))) | (g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))))),
% 18.25/18.41 inference(quant_inst,[status(thm)],[])).
% 18.25/18.41 tff(9,plain,
% 18.25/18.41 ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C))) | g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0)))),
% 18.25/18.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 18.25/18.41 tff(10,plain,
% 18.25/18.41 ($false),
% 18.25/18.41 inference(unit_resolution,[status(thm)],[9, 6, 4, 1])).
% 18.25/18.41 tff(11,plain,((g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))) | (~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C)))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.41 tff(12,plain,
% 18.25/18.41 (g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))),
% 18.25/18.41 inference(unit_resolution,[status(thm)],[11, 1])).
% 18.25/18.41 tff(13,assumption,((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))), introduced(assumption)).
% 18.25/18.41 tff(14,plain,
% 18.25/18.41 (^[B: $i] : refl((~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))) <=> (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))))),
% 18.25/18.41 inference(bind,[status(th)],[])).
% 18.25/18.41 tff(15,plain,
% 18.25/18.41 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.41 inference(quant_intro,[status(thm)],[14])).
% 18.25/18.41 tff(16,plain,
% 18.25/18.41 (^[B: $i] : rewrite((~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))) <=> (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))))),
% 18.25/18.41 inference(bind,[status(th)],[])).
% 18.25/18.41 tff(17,plain,
% 18.25/18.41 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.41 inference(quant_intro,[status(thm)],[16])).
% 18.25/18.41 tff(18,plain,
% 18.25/18.41 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.41 inference(transitivity,[status(thm)],[17, 15])).
% 18.25/18.41 tff(19,plain,
% 18.25/18.41 (^[B: $i] : trans(monotonicity(rewrite(((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) <=> ((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))), rewrite(((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) <=> ((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))), rewrite(((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))))) <=> ((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))), ((((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))) <=> (((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B))))))) & ((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B))))))) & ((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))))), rewrite((((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B))))))) & ((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B))))))) & ((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))))))) <=> (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))), ((((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))) <=> (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))))),
% 18.25/18.42 inference(bind,[status(th)],[])).
% 18.25/18.42 tff(20,plain,
% 18.25/18.42 (![B: $i] : (((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))) <=> ![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.42 inference(quant_intro,[status(thm)],[19])).
% 18.25/18.42 tff(21,plain,
% 18.25/18.42 (^[B: $i] : rewrite((((~g_true_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))) <=> (((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))))),
% 18.25/18.42 inference(bind,[status(th)],[])).
% 18.25/18.42 tff(22,plain,
% 18.25/18.42 (![B: $i] : (((~g_true_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))) <=> ![B: $i] : (((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))))))),
% 18.25/18.42 inference(quant_intro,[status(thm)],[21])).
% 18.25/18.42 tff(23,plain,
% 18.25/18.42 ((~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))) <=> (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.25/18.42 inference(rewrite,[status(thm)],[])).
% 18.25/18.42 tff(24,plain,
% 18.25/18.42 ((~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))))))) <=> (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.25/18.42 inference(rewrite,[status(thm)],[])).
% 18.25/18.42 tff(25,axiom,(~(![A: $i] : ?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))) | (?[A: $i] : (?[B: $i] : ((g_both(B, A) & ?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B)))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & ![C: $i] : (g_false_only(B, C) | g_false_only(C, B))) | (g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nc3')).
% 18.25/18.42 tff(26,plain,
% 18.25/18.42 (~![A: $i] : ?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))))))),
% 18.25/18.42 inference(or_elim,[status(thm)],[25])).
% 18.25/18.42 tff(27,plain,
% 18.25/18.42 (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[26, 24])).
% 18.25/18.42 tff(28,plain,
% 18.25/18.42 (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 18.25/18.42 tff(29,plain,
% 18.25/18.42 (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[28, 23])).
% 18.25/18.42 tff(30,plain,
% 18.25/18.42 (~![A: $i] : ?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[29, 23])).
% 18.25/18.42 tff(31,plain,(
% 18.25/18.42 $oeq((~?[B: $i] : ((g_true_only(B, A!0) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A!0) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A!0) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))), ![B: $i] : (((~g_true_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | ((![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B))))))))),
% 18.25/18.42 inference(transitivity,[status(sab)],[30])).
% 18.25/18.42 tff(32,plain,
% 18.25/18.42 (![B: $i] : (((~g_true_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_both(B, A!0)) | ((~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))) & ![C: $i] : (~(g_true_only(B, C) & g_true_only(C, B))))) & ((~g_false_only(B, A!0)) | (((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))))) & (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)))))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[31, 22])).
% 18.25/18.42 tff(33,plain,
% 18.25/18.42 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[32, 20])).
% 18.25/18.42 tff(34,plain,
% 18.25/18.42 (![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[33, 18])).
% 18.25/18.42 tff(35,plain,
% 18.25/18.42 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))))),
% 18.25/18.42 inference(rewrite,[status(thm)],[])).
% 18.25/18.42 tff(36,plain,
% 18.25/18.42 ((~((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))) <=> (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))),
% 18.25/18.42 inference(rewrite,[status(thm)],[])).
% 18.25/18.42 tff(37,plain,
% 18.25/18.42 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))))),
% 18.25/18.42 inference(monotonicity,[status(thm)],[36])).
% 18.25/18.42 tff(38,plain,
% 18.25/18.42 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))))),
% 18.25/18.42 inference(transitivity,[status(thm)],[37, 35])).
% 18.25/18.42 tff(39,plain,
% 18.25/18.42 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))),
% 18.25/18.42 inference(quant_inst,[status(thm)],[])).
% 18.25/18.42 tff(40,plain,
% 18.25/18.42 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))))),
% 18.25/18.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 18.25/18.42 tff(41,plain,
% 18.25/18.42 ($false),
% 18.25/18.42 inference(unit_resolution,[status(thm)],[40, 34, 13])).
% 18.25/18.42 tff(42,plain,(~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.42 tff(43,plain,
% 18.25/18.42 (((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))) | ((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))),
% 18.25/18.42 inference(tautology,[status(thm)],[])).
% 18.25/18.42 tff(44,plain,
% 18.25/18.42 ((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))))),
% 18.25/18.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 18.25/18.42 tff(45,plain,
% 18.25/18.42 ((~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))))),
% 18.25/18.42 inference(tautology,[status(thm)],[])).
% 18.25/18.42 tff(46,plain,
% 18.25/18.42 ((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))))),
% 18.25/18.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 18.25/18.42 tff(47,plain,
% 18.25/18.42 (~g_both(tptp_fun_B_3(A!0), A!0)),
% 18.25/18.42 inference(unit_resolution,[status(thm)],[46, 12])).
% 18.25/18.42 tff(48,plain,
% 18.25/18.42 (((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C)) | (~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))))))) | g_both(tptp_fun_B_3(A!0), A!0)),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(49,plain,
% 18.25/18.43 ((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C)) | (~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 18.25/18.43 tff(50,assumption,(![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))), introduced(assumption)).
% 18.25/18.43 tff(51,plain,
% 18.25/18.43 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))))))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(52,plain,
% 18.25/18.43 ((~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C)))))))))))) <=> (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))))))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(53,plain,
% 18.25/18.43 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))))))),
% 18.25/18.43 inference(monotonicity,[status(thm)],[52])).
% 18.25/18.43 tff(54,plain,
% 18.25/18.43 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))))))),
% 18.25/18.43 inference(transitivity,[status(thm)],[53, 51])).
% 18.25/18.43 tff(55,plain,
% 18.25/18.43 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | g_false_only(tptp_fun_C_1(A!0), C) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))))))))))))),
% 18.25/18.43 inference(quant_inst,[status(thm)],[])).
% 18.25/18.43 tff(56,plain,
% 18.25/18.43 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))))))),
% 18.25/18.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 18.25/18.43 tff(57,plain,
% 18.25/18.43 (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[56, 34])).
% 18.25/18.43 tff(58,plain,
% 18.25/18.43 (((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~g_both(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0)))))) | (~((~g_false_only(tptp_fun_C_1(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))) | g_false_only(tptp_fun_C_1(A!0), tptp_fun_C_2(tptp_fun_C_1(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))))) | ((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(59,plain,
% 18.25/18.43 ((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C))))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[58, 57])).
% 18.25/18.43 tff(60,assumption,(~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))), introduced(assumption)).
% 18.25/18.43 tff(61,plain,
% 18.25/18.43 (((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))) | g_true_only(tptp_fun_C_1(A!0), A!0)),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(62,plain,
% 18.25/18.43 (g_true_only(tptp_fun_C_1(A!0), A!0)),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 18.25/18.43 tff(63,plain,
% 18.25/18.43 ((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C))))))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(64,plain,
% 18.25/18.43 ((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))))) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C))))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[63, 62])).
% 18.25/18.43 tff(65,plain,
% 18.25/18.43 (~((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C)))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[64, 59])).
% 18.25/18.43 tff(66,plain,
% 18.25/18.43 (((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(A!0), tptp_fun_C_1(tptp_fun_C_1(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!0)), tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!0)) | (~(g_both(C, tptp_fun_C_1(A!0)) | g_both(tptp_fun_C_1(A!0), C))) | g_false_only(tptp_fun_C_1(A!0), C))))) | ![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(67,plain,
% 18.25/18.43 (![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 18.25/18.43 tff(68,plain,
% 18.25/18.43 (((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))) | g_true_only(A!0, tptp_fun_C_1(A!0))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(69,plain,
% 18.25/18.43 (g_true_only(A!0, tptp_fun_C_1(A!0))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[68, 60])).
% 18.25/18.43 tff(70,plain,
% 18.25/18.43 (((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | ((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(71,plain,
% 18.25/18.43 (((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0)))) <=> ((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(72,plain,
% 18.25/18.43 (((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | ((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | ((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))))),
% 18.25/18.43 inference(monotonicity,[status(thm)],[71])).
% 18.25/18.43 tff(73,plain,
% 18.25/18.43 (((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | ((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))),
% 18.25/18.43 inference(transitivity,[status(thm)],[72, 70])).
% 18.25/18.43 tff(74,plain,
% 18.25/18.43 ((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | ((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))),
% 18.25/18.43 inference(quant_inst,[status(thm)],[])).
% 18.25/18.43 tff(75,plain,
% 18.25/18.43 ((~![C: $i] : ((~g_true_only(tptp_fun_C_1(A!0), C)) | (~g_true_only(C, tptp_fun_C_1(A!0))))) | (~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))),
% 18.25/18.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 18.25/18.43 tff(76,plain,
% 18.25/18.43 ($false),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[75, 69, 62, 67])).
% 18.25/18.43 tff(77,plain,((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.43 tff(78,assumption,(~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))), introduced(assumption)).
% 18.25/18.43 tff(79,plain,
% 18.25/18.43 ((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))) | (~g_false_only(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(80,plain,
% 18.25/18.43 (~g_false_only(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[79, 78])).
% 18.25/18.43 tff(81,plain,
% 18.25/18.43 ((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))) | (~g_false_only(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(82,plain,
% 18.25/18.43 (~g_false_only(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[81, 78])).
% 18.25/18.43 tff(83,assumption,(~g_false_only(A!0, tptp_fun_C_2(A!0))), introduced(assumption)).
% 18.25/18.43 tff(84,assumption,((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))), introduced(assumption)).
% 18.25/18.43 tff(85,plain,
% 18.25/18.43 ((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))) | ((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(86,plain,
% 18.25/18.43 ((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[85, 78])).
% 18.25/18.43 tff(87,plain,
% 18.25/18.43 ((~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))),
% 18.25/18.43 inference(tautology,[status(thm)],[])).
% 18.25/18.43 tff(88,plain,
% 18.25/18.43 (![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))),
% 18.25/18.43 inference(unit_resolution,[status(thm)],[87, 86, 84])).
% 18.25/18.43 tff(89,plain,
% 18.25/18.43 (((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))) <=> ((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(90,plain,
% 18.25/18.43 ((g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))) <=> (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(91,plain,
% 18.25/18.43 ((~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))) <=> (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))),
% 18.25/18.43 inference(rewrite,[status(thm)],[])).
% 18.25/18.43 tff(92,plain,
% 18.25/18.43 ((g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))) <=> (g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.44 inference(monotonicity,[status(thm)],[91])).
% 18.25/18.44 tff(93,plain,
% 18.25/18.44 ((g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))) <=> (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.44 inference(transitivity,[status(thm)],[92, 90])).
% 18.25/18.44 tff(94,plain,
% 18.25/18.44 (((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))) <=> ((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))))),
% 18.25/18.44 inference(monotonicity,[status(thm)],[93])).
% 18.25/18.44 tff(95,plain,
% 18.25/18.44 (((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))) <=> ((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.44 inference(transitivity,[status(thm)],[94, 89])).
% 18.25/18.44 tff(96,plain,
% 18.25/18.44 ((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))))),
% 18.25/18.44 inference(quant_inst,[status(thm)],[])).
% 18.25/18.44 tff(97,plain,
% 18.25/18.44 ((~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 18.25/18.44 tff(98,plain,
% 18.25/18.44 (~(g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[97, 88, 83, 82])).
% 18.25/18.44 tff(99,plain,
% 18.25/18.44 ((g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))) | (~g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(tautology,[status(thm)],[])).
% 18.25/18.44 tff(100,plain,
% 18.25/18.44 (~g_both(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 18.25/18.44 tff(101,plain,
% 18.25/18.44 (^[X_2: $i, X_1: $i] : refl((g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)))),
% 18.25/18.44 inference(bind,[status(th)],[])).
% 18.25/18.44 tff(102,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(quant_intro,[status(thm)],[101])).
% 18.25/18.44 tff(103,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(104,plain,
% 18.25/18.44 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((g_true_only(X_2, X_1) | g_both(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)))), rewrite(((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))), (((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))))),
% 18.25/18.44 inference(bind,[status(th)],[])).
% 18.25/18.44 tff(105,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1)) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(quant_intro,[status(thm)],[104])).
% 18.25/18.44 tff(106,axiom,(![X_2: $i, X_1: $i] : ((g_true_only(X_2, X_1) | g_both(X_2, X_1)) | g_false_only(X_2, X_1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exhaustion_g')).
% 18.25/18.44 tff(107,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 18.25/18.44 tff(108,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[107, 103])).
% 18.25/18.44 tff(109,plain,(
% 18.25/18.44 ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(skolemize,[status(sab)],[108])).
% 18.25/18.44 tff(110,plain,
% 18.25/18.44 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[109, 102])).
% 18.25/18.44 tff(111,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(112,plain,
% 18.25/18.44 ((g_true_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0))) <=> (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(113,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(monotonicity,[status(thm)],[112])).
% 18.25/18.44 tff(114,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(transitivity,[status(thm)],[113, 111])).
% 18.25/18.44 tff(115,plain,
% 18.25/18.44 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(quant_inst,[status(thm)],[])).
% 18.25/18.44 tff(116,plain,
% 18.25/18.44 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 18.25/18.44 tff(117,plain,
% 18.25/18.44 (g_true_only(A!0, tptp_fun_C_2(A!0)) | g_both(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[116, 110, 83])).
% 18.25/18.44 tff(118,plain,
% 18.25/18.44 (g_true_only(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[117, 100])).
% 18.25/18.44 tff(119,plain,
% 18.25/18.44 ((g_both(tptp_fun_C_2(A!0), A!0) | g_both(A!0, tptp_fun_C_2(A!0))) | (~g_both(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.44 inference(tautology,[status(thm)],[])).
% 18.25/18.44 tff(120,plain,
% 18.25/18.44 (~g_both(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[119, 98])).
% 18.25/18.44 tff(121,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(122,plain,
% 18.25/18.44 ((g_true_only(tptp_fun_C_2(A!0), A!0) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0)) <=> (g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(123,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_C_2(A!0), A!0) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0)))),
% 18.25/18.44 inference(monotonicity,[status(thm)],[122])).
% 18.25/18.44 tff(124,plain,
% 18.25/18.44 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_C_2(A!0), A!0) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.44 inference(transitivity,[status(thm)],[123, 121])).
% 18.25/18.44 tff(125,plain,
% 18.25/18.44 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(tptp_fun_C_2(A!0), A!0) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.44 inference(quant_inst,[status(thm)],[])).
% 18.25/18.44 tff(126,plain,
% 18.25/18.44 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(tptp_fun_C_2(A!0), A!0) | g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 18.25/18.44 tff(127,plain,
% 18.25/18.44 (g_both(tptp_fun_C_2(A!0), A!0) | g_true_only(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[126, 110, 82])).
% 18.25/18.44 tff(128,plain,
% 18.25/18.44 (g_true_only(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[127, 120])).
% 18.25/18.44 tff(129,plain,
% 18.25/18.44 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))))))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(130,plain,
% 18.25/18.44 ((~((~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C)))))))))))) <=> (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))))))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(131,plain,
% 18.25/18.44 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))))))),
% 18.25/18.44 inference(monotonicity,[status(thm)],[130])).
% 18.25/18.44 tff(132,plain,
% 18.25/18.44 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))))))),
% 18.25/18.44 inference(transitivity,[status(thm)],[131, 129])).
% 18.25/18.44 tff(133,plain,
% 18.25/18.44 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C)))))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(C, tptp_fun_C_2(A!0)) | g_both(tptp_fun_C_2(A!0), C))))))))))))),
% 18.25/18.44 inference(quant_inst,[status(thm)],[])).
% 18.25/18.44 tff(134,plain,
% 18.25/18.44 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))))))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 18.25/18.44 tff(135,plain,
% 18.25/18.44 (~((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[134, 34])).
% 18.25/18.44 tff(136,plain,
% 18.25/18.44 (((~((~g_both(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))))))) | (~((~g_false_only(tptp_fun_C_2(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), tptp_fun_C_2(tptp_fun_C_2(A!0))) | g_false_only(tptp_fun_C_2(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))))) | ((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))),
% 18.25/18.44 inference(tautology,[status(thm)],[])).
% 18.25/18.44 tff(137,plain,
% 18.25/18.44 ((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[136, 135])).
% 18.25/18.44 tff(138,plain,
% 18.25/18.44 ((~((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))))) | (~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))))),
% 18.25/18.44 inference(tautology,[status(thm)],[])).
% 18.25/18.44 tff(139,plain,
% 18.25/18.44 (~((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0))))))))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[138, 128, 137])).
% 18.25/18.44 tff(140,plain,
% 18.25/18.44 (((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_2(A!0)), tptp_fun_C_2(A!0))) | (~g_true_only(tptp_fun_C_2(A!0), tptp_fun_C_1(tptp_fun_C_2(A!0)))))) | ![C: $i] : (g_false_only(C, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), C) | (~(g_both(tptp_fun_C_2(A!0), C) | g_both(C, tptp_fun_C_2(A!0)))))))) | ![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(tautology,[status(thm)],[])).
% 18.25/18.44 tff(141,plain,
% 18.25/18.44 (![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 18.25/18.44 tff(142,plain,
% 18.25/18.44 (((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | ((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_2(A!0))))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(rewrite,[status(thm)],[])).
% 18.25/18.44 tff(143,plain,
% 18.25/18.44 ((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | ((~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_2(A!0))))),
% 18.25/18.44 inference(quant_inst,[status(thm)],[])).
% 18.25/18.44 tff(144,plain,
% 18.25/18.44 ((~![C: $i] : ((~g_true_only(tptp_fun_C_2(A!0), C)) | (~g_true_only(C, tptp_fun_C_2(A!0))))) | (~g_true_only(tptp_fun_C_2(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 18.25/18.44 tff(145,plain,
% 18.25/18.44 ($false),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[144, 141, 128, 118])).
% 18.25/18.44 tff(146,plain,((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.44 tff(147,plain,
% 18.25/18.44 ($false),
% 18.25/18.44 inference(unit_resolution,[status(thm)],[146, 80, 78, 77])).
% 18.25/18.44 tff(148,plain,(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.44 tff(149,plain,
% 18.25/18.44 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))))))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(150,plain,
% 18.25/18.45 ((~((~((~g_true_only(A!0, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))))) <=> (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(151,plain,
% 18.25/18.45 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))))))),
% 18.25/18.45 inference(monotonicity,[status(thm)],[150])).
% 18.25/18.45 tff(152,plain,
% 18.25/18.45 (((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))) <=> ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))))))),
% 18.25/18.45 inference(transitivity,[status(thm)],[151, 149])).
% 18.25/18.45 tff(153,plain,
% 18.25/18.45 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(tptp_fun_C_2(A!0), A!0) | g_false_only(A!0, tptp_fun_C_2(A!0)) | (~((~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))),
% 18.25/18.45 inference(quant_inst,[status(thm)],[])).
% 18.25/18.45 tff(154,plain,
% 18.25/18.45 ((~![B: $i] : (~((~((~g_true_only(B, A!0)) | (~((~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_both(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~![C: $i] : ((~g_true_only(B, C)) | (~g_true_only(C, B)))))))) | (~((~g_false_only(B, A!0)) | (~(g_false_only(tptp_fun_C_2(B), B) | g_false_only(B, tptp_fun_C_2(B)) | (~((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C))))))))))))) | (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))))),
% 18.25/18.45 inference(modus_ponens,[status(thm)],[153, 152])).
% 18.25/18.45 tff(155,plain,
% 18.25/18.45 (~((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[154, 34])).
% 18.25/18.45 tff(156,plain,
% 18.25/18.45 (((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))) | ((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(157,plain,
% 18.25/18.45 ((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[156, 155])).
% 18.25/18.45 tff(158,plain,
% 18.25/18.45 ((~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(159,plain,
% 18.25/18.45 ((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[158, 157])).
% 18.25/18.45 tff(160,plain,
% 18.25/18.45 (~g_false_only(A!0, A!0)),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[159, 148])).
% 18.25/18.45 tff(161,assumption,(g_true_only(A!0, A!0)), introduced(assumption)).
% 18.25/18.45 tff(162,plain,
% 18.25/18.45 (((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))) | ((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(163,plain,
% 18.25/18.45 ((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[162, 155])).
% 18.25/18.45 tff(164,plain,
% 18.25/18.45 ((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(165,plain,
% 18.25/18.45 ((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 18.25/18.45 tff(166,plain,
% 18.25/18.45 (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[165, 161])).
% 18.25/18.45 tff(167,plain,
% 18.25/18.45 (((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))) | ![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(168,plain,
% 18.25/18.45 (![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[167, 166])).
% 18.25/18.45 tff(169,plain,
% 18.25/18.45 (((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~g_true_only(A!0, A!0))) <=> ((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~g_true_only(A!0, A!0)))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(170,plain,
% 18.25/18.45 (((~g_true_only(A!0, A!0)) | (~g_true_only(A!0, A!0))) <=> (~g_true_only(A!0, A!0))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(171,plain,
% 18.25/18.45 (((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | ((~g_true_only(A!0, A!0)) | (~g_true_only(A!0, A!0)))) <=> ((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~g_true_only(A!0, A!0)))),
% 18.25/18.45 inference(monotonicity,[status(thm)],[170])).
% 18.25/18.45 tff(172,plain,
% 18.25/18.45 (((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | ((~g_true_only(A!0, A!0)) | (~g_true_only(A!0, A!0)))) <=> ((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~g_true_only(A!0, A!0)))),
% 18.25/18.45 inference(transitivity,[status(thm)],[171, 169])).
% 18.25/18.45 tff(173,plain,
% 18.25/18.45 ((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | ((~g_true_only(A!0, A!0)) | (~g_true_only(A!0, A!0)))),
% 18.25/18.45 inference(quant_inst,[status(thm)],[])).
% 18.25/18.45 tff(174,plain,
% 18.25/18.45 ((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~g_true_only(A!0, A!0))),
% 18.25/18.45 inference(modus_ponens,[status(thm)],[173, 172])).
% 18.25/18.45 tff(175,plain,
% 18.25/18.45 ($false),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[174, 161, 168])).
% 18.25/18.45 tff(176,plain,(~g_true_only(A!0, A!0)), inference(lemma,lemma(discharge,[]))).
% 18.25/18.45 tff(177,plain,
% 18.25/18.45 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(178,plain,
% 18.25/18.45 ((g_true_only(A!0, A!0) | g_false_only(A!0, A!0) | g_both(A!0, A!0)) <=> (g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0))),
% 18.25/18.45 inference(rewrite,[status(thm)],[])).
% 18.25/18.45 tff(179,plain,
% 18.25/18.45 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, A!0) | g_false_only(A!0, A!0) | g_both(A!0, A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0)))),
% 18.25/18.45 inference(monotonicity,[status(thm)],[178])).
% 18.25/18.45 tff(180,plain,
% 18.25/18.45 (((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, A!0) | g_false_only(A!0, A!0) | g_both(A!0, A!0))) <=> ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0))),
% 18.25/18.45 inference(transitivity,[status(thm)],[179, 177])).
% 18.25/18.45 tff(181,plain,
% 18.25/18.45 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | (g_true_only(A!0, A!0) | g_false_only(A!0, A!0) | g_both(A!0, A!0))),
% 18.25/18.45 inference(quant_inst,[status(thm)],[])).
% 18.25/18.45 tff(182,plain,
% 18.25/18.45 ((~![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) | g_false_only(X_2, X_1) | g_both(X_2, X_1))) | g_false_only(A!0, A!0) | g_both(A!0, A!0) | g_true_only(A!0, A!0)),
% 18.25/18.45 inference(modus_ponens,[status(thm)],[181, 180])).
% 18.25/18.45 tff(183,plain,
% 18.25/18.45 (g_false_only(A!0, A!0) | g_both(A!0, A!0)),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[182, 110, 176])).
% 18.25/18.45 tff(184,plain,
% 18.25/18.45 (g_both(A!0, A!0)),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[183, 160])).
% 18.25/18.45 tff(185,plain,
% 18.25/18.45 (((~((~g_true_only(A!0, A!0)) | (~((~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))))) | (~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~((~g_false_only(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))))))) | ((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(186,plain,
% 18.25/18.45 ((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[185, 155])).
% 18.25/18.45 tff(187,plain,
% 18.25/18.45 ((~((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))))) | (~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(188,plain,
% 18.25/18.45 ((~g_both(A!0, A!0)) | (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0))))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[187, 186])).
% 18.25/18.45 tff(189,plain,
% 18.25/18.45 (~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0)))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[188, 184])).
% 18.25/18.45 tff(190,plain,
% 18.25/18.45 ((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0))))) | (~g_false_only(A!0, tptp_fun_C_2(A!0)))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(191,plain,
% 18.25/18.45 (~g_false_only(A!0, tptp_fun_C_2(A!0))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[190, 189])).
% 18.25/18.45 tff(192,plain,
% 18.25/18.45 ((g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~![C: $i] : ((~g_true_only(A!0, C)) | (~g_true_only(C, A!0))))) | (~g_false_only(tptp_fun_C_2(A!0), A!0))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(193,plain,
% 18.25/18.45 (~g_false_only(tptp_fun_C_2(A!0), A!0)),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[192, 189])).
% 18.25/18.45 tff(194,plain,
% 18.25/18.45 ((~(g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))))) | g_false_only(A!0, tptp_fun_C_2(A!0)) | g_false_only(tptp_fun_C_2(A!0), A!0) | (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))),
% 18.25/18.45 inference(tautology,[status(thm)],[])).
% 18.25/18.45 tff(195,plain,
% 18.25/18.45 (~((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.45 inference(unit_resolution,[status(thm)],[194, 193, 148, 191])).
% 18.25/18.45 tff(196,plain,
% 18.25/18.45 (((~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) | (~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(197,plain,
% 18.25/18.46 (~![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[196, 195])).
% 18.25/18.46 tff(198,plain,
% 18.25/18.46 (((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ((~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) <=> ((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(199,plain,
% 18.25/18.46 (((~g_both(A!0, A!0)) | (~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))) <=> ((~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(200,plain,
% 18.25/18.46 (((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ((~g_both(A!0, A!0)) | (~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) <=> ((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ((~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))))),
% 18.25/18.46 inference(monotonicity,[status(thm)],[199])).
% 18.25/18.46 tff(201,plain,
% 18.25/18.46 (((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ((~g_both(A!0, A!0)) | (~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))) <=> ((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.46 inference(transitivity,[status(thm)],[200, 198])).
% 18.25/18.46 tff(202,plain,
% 18.25/18.46 ((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ((~g_both(A!0, A!0)) | (~((~g_true_only(tptp_fun_C_1(A!0), A!0)) | (~g_true_only(A!0, tptp_fun_C_1(A!0))))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C)))))),
% 18.25/18.46 inference(quant_inst,[status(thm)],[])).
% 18.25/18.46 tff(203,plain,
% 18.25/18.46 ((~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | (~g_both(A!0, A!0)) | (~((~g_true_only(A!0, tptp_fun_C_1(A!0))) | (~g_true_only(tptp_fun_C_1(A!0), A!0)))) | ![C: $i] : (g_false_only(C, A!0) | g_false_only(A!0, C) | (~(g_both(C, A!0) | g_both(A!0, C))))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 18.25/18.46 tff(204,plain,
% 18.25/18.46 ($false),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[203, 77, 197, 184, 50])).
% 18.25/18.46 tff(205,plain,(~![B: $i] : ((~g_both(B, A!0)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.46 tff(206,assumption,(~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))))))), introduced(assumption)).
% 18.25/18.46 tff(207,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))))) | ((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(208,plain,
% 18.25/18.46 ((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[207, 206])).
% 18.25/18.46 tff(209,plain,
% 18.25/18.46 (~((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[40, 34])).
% 18.25/18.46 tff(210,plain,
% 18.25/18.46 (((~((~g_false_only(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~g_both(tptp_fun_B_3(A!0), A!0)) | (~(g_false_only(tptp_fun_C_2(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_2(tptp_fun_B_3(A!0))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))))))) | (~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))))) | ((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(211,plain,
% 18.25/18.46 ((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[210, 209])).
% 18.25/18.46 tff(212,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))))) | g_true_only(tptp_fun_B_3(A!0), A!0)),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(213,plain,
% 18.25/18.46 (g_true_only(tptp_fun_B_3(A!0), A!0)),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[212, 206])).
% 18.25/18.46 tff(214,plain,
% 18.25/18.46 ((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(215,plain,
% 18.25/18.46 ((~((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))))) | (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[214, 213])).
% 18.25/18.46 tff(216,plain,
% 18.25/18.46 (~((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[215, 211])).
% 18.25/18.46 tff(217,plain,
% 18.25/18.46 (((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))) | ![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(218,plain,
% 18.25/18.46 (![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[217, 216])).
% 18.25/18.46 tff(219,assumption,(![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))), introduced(assumption)).
% 18.25/18.46 tff(220,assumption,(~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))), introduced(assumption)).
% 18.25/18.46 tff(221,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))) | g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(222,plain,
% 18.25/18.46 (g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[221, 220])).
% 18.25/18.46 tff(223,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))) | g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(224,plain,
% 18.25/18.46 (g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[223, 220])).
% 18.25/18.46 tff(225,plain,
% 18.25/18.46 (((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(226,plain,
% 18.25/18.46 ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(quant_inst,[status(thm)],[])).
% 18.25/18.46 tff(227,plain,
% 18.25/18.46 ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[226, 225])).
% 18.25/18.46 tff(228,plain,
% 18.25/18.46 ($false),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[227, 224, 222, 219])).
% 18.25/18.46 tff(229,plain,(((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.46 tff(230,plain,
% 18.25/18.46 ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[229, 218])).
% 18.25/18.46 tff(231,plain,
% 18.25/18.46 ((~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))))) | (~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(232,plain,
% 18.25/18.46 (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[231, 230, 208])).
% 18.25/18.46 tff(233,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))) | (~g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(234,plain,
% 18.25/18.46 (~g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[233, 232])).
% 18.25/18.46 tff(235,plain,
% 18.25/18.46 (((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))))) | ((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(236,plain,
% 18.25/18.46 ((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[235, 216])).
% 18.25/18.46 tff(237,assumption,(~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))), introduced(assumption)).
% 18.25/18.46 tff(238,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))) | g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(239,plain,
% 18.25/18.46 (g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[238, 237])).
% 18.25/18.46 tff(240,plain,
% 18.25/18.46 (((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))) | g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(241,plain,
% 18.25/18.46 (g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[240, 237])).
% 18.25/18.46 tff(242,plain,
% 18.25/18.46 (((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) <=> ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(243,plain,
% 18.25/18.46 ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(quant_inst,[status(thm)],[])).
% 18.25/18.46 tff(244,plain,
% 18.25/18.46 ((~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[243, 242])).
% 18.25/18.46 tff(245,plain,
% 18.25/18.46 ($false),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[244, 241, 239, 219])).
% 18.25/18.46 tff(246,plain,(((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0)))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.46 tff(247,plain,
% 18.25/18.46 ((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[246, 218])).
% 18.25/18.46 tff(248,plain,
% 18.25/18.46 ((~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C)))))) | (~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_1(tptp_fun_B_3(A!0)))) | (~g_true_only(tptp_fun_C_1(tptp_fun_B_3(A!0)), tptp_fun_B_3(A!0))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(249,plain,
% 18.25/18.46 (![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[248, 247, 236])).
% 18.25/18.46 tff(250,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))) | (~g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(251,plain,
% 18.25/18.46 (~g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[250, 232])).
% 18.25/18.46 tff(252,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))) | (g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))),
% 18.25/18.46 inference(tautology,[status(thm)],[])).
% 18.25/18.46 tff(253,plain,
% 18.25/18.46 (g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[252, 232])).
% 18.25/18.46 tff(254,assumption,(![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))), introduced(assumption)).
% 18.25/18.46 tff(255,assumption,(~g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))), introduced(assumption)).
% 18.25/18.46 tff(256,assumption,(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))), introduced(assumption)).
% 18.25/18.46 tff(257,assumption,(~g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))), introduced(assumption)).
% 18.25/18.46 tff(258,plain,
% 18.25/18.46 (((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | (g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))) <=> ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(259,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))))) <=> (g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(260,plain,
% 18.25/18.46 ((~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) <=> (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(261,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))))) <=> (g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))))),
% 18.25/18.46 inference(monotonicity,[status(thm)],[260])).
% 18.25/18.46 tff(262,plain,
% 18.25/18.46 ((g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0))))) <=> (g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(transitivity,[status(thm)],[261, 259])).
% 18.25/18.46 tff(263,plain,
% 18.25/18.46 (((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | (g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))))) <=> ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | (g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))),
% 18.25/18.46 inference(monotonicity,[status(thm)],[262])).
% 18.25/18.46 tff(264,plain,
% 18.25/18.46 (((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | (g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))))) <=> ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)))),
% 18.25/18.46 inference(transitivity,[status(thm)],[263, 258])).
% 18.25/18.46 tff(265,plain,
% 18.25/18.46 ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | (g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))))),
% 18.25/18.46 inference(quant_inst,[status(thm)],[])).
% 18.25/18.46 tff(266,plain,
% 18.25/18.46 ((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[265, 264])).
% 18.25/18.46 tff(267,plain,
% 18.25/18.46 ($false),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[266, 257, 256, 255, 254])).
% 18.25/18.46 tff(268,plain,((~![C: $i] : (g_false_only(C, tptp_fun_B_3(A!0)) | g_false_only(tptp_fun_B_3(A!0), C) | (~(g_both(C, tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), C))))) | g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.46 tff(269,plain,
% 18.25/18.46 ($false),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[268, 253, 251, 249, 234])).
% 18.25/18.46 tff(270,plain,((~g_true_only(tptp_fun_B_3(A!0), A!0)) | (~((~((~g_true_only(tptp_fun_B_3(A!0), tptp_fun_C_5(A!0))) | (~g_true_only(tptp_fun_C_5(A!0), tptp_fun_B_3(A!0))))) | (~(g_false_only(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A!0), C)) | (~g_true_only(C, tptp_fun_B_3(A!0))))) | (~(g_both(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0)) | g_both(tptp_fun_B_3(A!0), tptp_fun_C_4(A!0)))) | g_false_only(tptp_fun_C_4(A!0), tptp_fun_B_3(A!0))))))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.46 tff(271,plain,
% 18.25/18.46 (^[X_2: $i, X_1: $i] : refl((~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1))) <=> (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1))))),
% 18.25/18.46 inference(bind,[status(th)],[])).
% 18.25/18.46 tff(272,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))),
% 18.25/18.46 inference(quant_intro,[status(thm)],[271])).
% 18.25/18.46 tff(273,plain,
% 18.25/18.46 (^[X_2: $i, X_1: $i] : trans(trans(monotonicity(rewrite((g_false(X_2, X_1) & (~g_true(X_2, X_1))) <=> (~((~g_false(X_2, X_1)) | g_true(X_2, X_1)))), ((g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1)))) <=> (g_false_only(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | g_true(X_2, X_1)))))), rewrite((g_false_only(X_2, X_1) <=> (~((~g_false(X_2, X_1)) | g_true(X_2, X_1)))) <=> (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))), ((g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1)))) <=> (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1))))), rewrite((~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1))) <=> (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))), ((g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1)))) <=> (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))))),
% 18.25/18.46 inference(bind,[status(th)],[])).
% 18.25/18.46 tff(274,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))),
% 18.25/18.46 inference(quant_intro,[status(thm)],[273])).
% 18.25/18.46 tff(275,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(276,axiom,(![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','false_only_g')).
% 18.25/18.46 tff(277,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1))))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[276, 275])).
% 18.25/18.46 tff(278,plain,(
% 18.25/18.46 ![X_2: $i, X_1: $i] : (g_false_only(X_2, X_1) <=> (g_false(X_2, X_1) & (~g_true(X_2, X_1))))),
% 18.25/18.46 inference(skolemize,[status(sab)],[277])).
% 18.25/18.46 tff(279,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[278, 274])).
% 18.25/18.46 tff(280,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[279, 272])).
% 18.25/18.46 tff(281,plain,
% 18.25/18.46 ((~![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))) | (~(((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))) <=> g_false_only(A!6, tptp_fun_C_1(A!6))))),
% 18.25/18.46 inference(quant_inst,[status(thm)],[])).
% 18.25/18.46 tff(282,plain,
% 18.25/18.46 (~(((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))) <=> g_false_only(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.46 inference(unit_resolution,[status(thm)],[281, 280])).
% 18.25/18.46 tff(283,plain,
% 18.25/18.46 (^[X_2: $i, X_1: $i] : refl((~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1))) <=> (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1))))),
% 18.25/18.46 inference(bind,[status(th)],[])).
% 18.25/18.46 tff(284,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1))) <=> ![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))),
% 18.25/18.46 inference(quant_intro,[status(thm)],[283])).
% 18.25/18.46 tff(285,plain,
% 18.25/18.46 (^[X_2: $i, X_1: $i] : trans(trans(monotonicity(rewrite((g_true(X_2, X_1) & (~g_false(X_2, X_1))) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))), ((g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> (g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))))), rewrite((g_true_only(X_2, X_1) <=> (~((~g_true(X_2, X_1)) | g_false(X_2, X_1)))) <=> (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))), ((g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1))))), rewrite((~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1))) <=> (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))), ((g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))))),
% 18.25/18.46 inference(bind,[status(th)],[])).
% 18.25/18.46 tff(286,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))),
% 18.25/18.46 inference(quant_intro,[status(thm)],[285])).
% 18.25/18.46 tff(287,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1)))) <=> ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 18.25/18.46 inference(rewrite,[status(thm)],[])).
% 18.25/18.46 tff(288,axiom,(![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','true_only_g')).
% 18.25/18.46 tff(289,plain,
% 18.25/18.46 (![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 18.25/18.46 inference(modus_ponens,[status(thm)],[288, 287])).
% 18.25/18.46 tff(290,plain,(
% 18.25/18.46 ![X_2: $i, X_1: $i] : (g_true_only(X_2, X_1) <=> (g_true(X_2, X_1) & (~g_false(X_2, X_1))))),
% 18.25/18.47 inference(skolemize,[status(sab)],[289])).
% 18.25/18.47 tff(291,plain,
% 18.25/18.47 (![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))),
% 18.25/18.47 inference(modus_ponens,[status(thm)],[290, 286])).
% 18.25/18.47 tff(292,plain,
% 18.25/18.47 (![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))),
% 18.25/18.47 inference(modus_ponens,[status(thm)],[291, 284])).
% 18.25/18.47 tff(293,plain,
% 18.25/18.47 ((~![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))) | (~(((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))) <=> g_true_only(A!6, tptp_fun_C_1(A!6))))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(294,plain,
% 18.25/18.47 (~(((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))) <=> g_true_only(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[293, 292])).
% 18.25/18.47 tff(295,assumption,(![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))), introduced(assumption)).
% 18.25/18.47 tff(296,assumption,(~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))), introduced(assumption)).
% 18.25/18.47 tff(297,plain,
% 18.25/18.47 (((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))) | ![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(298,plain,
% 18.25/18.47 (![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[297, 296])).
% 18.25/18.47 tff(299,plain,
% 18.25/18.47 ((~![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))) | (~(((~g_false(A!6, A!6)) | g_true(A!6, A!6)) <=> g_false_only(A!6, A!6)))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(300,plain,
% 18.25/18.47 (~(((~g_false(A!6, A!6)) | g_true(A!6, A!6)) <=> g_false_only(A!6, A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[299, 280])).
% 18.25/18.47 tff(301,plain,
% 18.25/18.47 ((~![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))) | (~(((~g_true(A!6, A!6)) | g_false(A!6, A!6)) <=> g_true_only(A!6, A!6)))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(302,plain,
% 18.25/18.47 (~(((~g_true(A!6, A!6)) | g_false(A!6, A!6)) <=> g_true_only(A!6, A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[301, 292])).
% 18.25/18.47 tff(303,plain,
% 18.25/18.47 (((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))) | g_true_only(A!6, A!6)),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(304,plain,
% 18.25/18.47 (g_true_only(A!6, A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[303, 296])).
% 18.25/18.47 tff(305,plain,
% 18.25/18.47 ((((~g_true(A!6, A!6)) | g_false(A!6, A!6)) <=> g_true_only(A!6, A!6)) | (~((~g_true(A!6, A!6)) | g_false(A!6, A!6))) | (~g_true_only(A!6, A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(306,plain,
% 18.25/18.47 ((((~g_true(A!6, A!6)) | g_false(A!6, A!6)) <=> g_true_only(A!6, A!6)) | (~((~g_true(A!6, A!6)) | g_false(A!6, A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[305, 304])).
% 18.25/18.47 tff(307,plain,
% 18.25/18.47 (~((~g_true(A!6, A!6)) | g_false(A!6, A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[306, 302])).
% 18.25/18.47 tff(308,plain,
% 18.25/18.47 (((~g_true(A!6, A!6)) | g_false(A!6, A!6)) | (~g_false(A!6, A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(309,plain,
% 18.25/18.47 (~g_false(A!6, A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[308, 307])).
% 18.25/18.47 tff(310,plain,
% 18.25/18.47 (((~g_false(A!6, A!6)) | g_true(A!6, A!6)) | g_false(A!6, A!6)),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(311,plain,
% 18.25/18.47 ((~g_false(A!6, A!6)) | g_true(A!6, A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[310, 309])).
% 18.25/18.47 tff(312,plain,
% 18.25/18.47 ((((~g_false(A!6, A!6)) | g_true(A!6, A!6)) <=> g_false_only(A!6, A!6)) | (~((~g_false(A!6, A!6)) | g_true(A!6, A!6))) | (~g_false_only(A!6, A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(313,plain,
% 18.25/18.47 ((((~g_false(A!6, A!6)) | g_true(A!6, A!6)) <=> g_false_only(A!6, A!6)) | (~g_false_only(A!6, A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[312, 311])).
% 18.25/18.47 tff(314,plain,
% 18.25/18.47 (~g_false_only(A!6, A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[313, 300])).
% 18.25/18.47 tff(315,plain,
% 18.25/18.47 (((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | g_false_only(A!6, A!6)) <=> ((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | g_false_only(A!6, A!6))),
% 18.25/18.47 inference(rewrite,[status(thm)],[])).
% 18.25/18.47 tff(316,plain,
% 18.25/18.47 ((g_false_only(A!6, A!6) | g_false_only(A!6, A!6)) <=> g_false_only(A!6, A!6)),
% 18.25/18.47 inference(rewrite,[status(thm)],[])).
% 18.25/18.47 tff(317,plain,
% 18.25/18.47 (((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | (g_false_only(A!6, A!6) | g_false_only(A!6, A!6))) <=> ((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | g_false_only(A!6, A!6))),
% 18.25/18.47 inference(monotonicity,[status(thm)],[316])).
% 18.25/18.47 tff(318,plain,
% 18.25/18.47 (((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | (g_false_only(A!6, A!6) | g_false_only(A!6, A!6))) <=> ((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | g_false_only(A!6, A!6))),
% 18.25/18.47 inference(transitivity,[status(thm)],[317, 315])).
% 18.25/18.47 tff(319,plain,
% 18.25/18.47 ((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | (g_false_only(A!6, A!6) | g_false_only(A!6, A!6))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(320,plain,
% 18.25/18.47 ((~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))) | g_false_only(A!6, A!6)),
% 18.25/18.47 inference(modus_ponens,[status(thm)],[319, 318])).
% 18.25/18.47 tff(321,plain,
% 18.25/18.47 ($false),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[320, 314, 298])).
% 18.25/18.47 tff(322,plain,((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))), inference(lemma,lemma(discharge,[]))).
% 18.25/18.47 tff(323,plain,
% 18.25/18.47 (((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))) <=> ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))),
% 18.25/18.47 inference(rewrite,[status(thm)],[])).
% 18.25/18.47 tff(324,plain,
% 18.25/18.47 (((~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_false_only(A!6, A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))))) <=> ((~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))),
% 18.25/18.47 inference(rewrite,[status(thm)],[])).
% 18.25/18.47 tff(325,plain,
% 18.25/18.47 (((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_false_only(A!6, A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))) <=> ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))))))),
% 18.25/18.47 inference(monotonicity,[status(thm)],[324])).
% 18.25/18.47 tff(326,plain,
% 18.25/18.47 (((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_false_only(A!6, A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))) <=> ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))),
% 18.25/18.47 inference(transitivity,[status(thm)],[325, 323])).
% 18.25/18.47 tff(327,plain,
% 18.25/18.47 ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_false_only(A!6, A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C))))))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(328,plain,
% 18.25/18.47 ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(A!6, A!6)) | (~![C: $i] : (g_false_only(C, A!6) | g_false_only(A!6, C)))))),
% 18.25/18.47 inference(modus_ponens,[status(thm)],[327, 326])).
% 18.25/18.47 tff(329,plain,
% 18.25/18.47 ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6))))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[328, 322])).
% 18.25/18.47 tff(330,plain,
% 18.25/18.47 (~((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[329, 295])).
% 18.25/18.47 tff(331,plain,
% 18.25/18.47 (((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6))) | g_true_only(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(332,plain,
% 18.25/18.47 (g_true_only(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[331, 330])).
% 18.25/18.47 tff(333,plain,
% 18.25/18.47 ((((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))) <=> g_true_only(A!6, tptp_fun_C_1(A!6))) | (~((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6)))) | (~g_true_only(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(334,plain,
% 18.25/18.47 ((((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))) <=> g_true_only(A!6, tptp_fun_C_1(A!6))) | (~((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[333, 332])).
% 18.25/18.47 tff(335,plain,
% 18.25/18.47 (~((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[334, 294])).
% 18.25/18.47 tff(336,plain,
% 18.25/18.47 (((~g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))) | (~g_false(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(337,plain,
% 18.25/18.47 (~g_false(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[336, 335])).
% 18.25/18.47 tff(338,plain,
% 18.25/18.47 (((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))) | g_false(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(339,plain,
% 18.25/18.47 ((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[338, 337])).
% 18.25/18.47 tff(340,plain,
% 18.25/18.47 ((((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))) <=> g_false_only(A!6, tptp_fun_C_1(A!6))) | (~((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6)))) | (~g_false_only(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(341,plain,
% 18.25/18.47 ((((~g_false(A!6, tptp_fun_C_1(A!6))) | g_true(A!6, tptp_fun_C_1(A!6))) <=> g_false_only(A!6, tptp_fun_C_1(A!6))) | (~g_false_only(A!6, tptp_fun_C_1(A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[340, 339])).
% 18.25/18.47 tff(342,plain,
% 18.25/18.47 (~g_false_only(A!6, tptp_fun_C_1(A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[341, 282])).
% 18.25/18.47 tff(343,plain,
% 18.25/18.47 ((~![X_2: $i, X_1: $i] : (~(((~g_false(X_2, X_1)) | g_true(X_2, X_1)) <=> g_false_only(X_2, X_1)))) | (~(((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)) <=> g_false_only(tptp_fun_C_1(A!6), A!6)))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(344,plain,
% 18.25/18.47 (~(((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)) <=> g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[343, 280])).
% 18.25/18.47 tff(345,plain,
% 18.25/18.47 ((~![X_2: $i, X_1: $i] : (~(((~g_true(X_2, X_1)) | g_false(X_2, X_1)) <=> g_true_only(X_2, X_1)))) | (~(((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)) <=> g_true_only(tptp_fun_C_1(A!6), A!6)))),
% 18.25/18.47 inference(quant_inst,[status(thm)],[])).
% 18.25/18.47 tff(346,plain,
% 18.25/18.47 (~(((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)) <=> g_true_only(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[345, 292])).
% 18.25/18.47 tff(347,plain,
% 18.25/18.47 (((~g_false_only(A!6, A!6)) | (~g_true_only(A!6, tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6))) | g_true_only(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(348,plain,
% 18.25/18.47 (g_true_only(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[347, 330])).
% 18.25/18.47 tff(349,plain,
% 18.25/18.47 ((((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)) <=> g_true_only(tptp_fun_C_1(A!6), A!6)) | (~((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6))) | (~g_true_only(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(350,plain,
% 18.25/18.47 ((((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)) <=> g_true_only(tptp_fun_C_1(A!6), A!6)) | (~((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[349, 348])).
% 18.25/18.47 tff(351,plain,
% 18.25/18.47 (~((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[350, 346])).
% 18.25/18.47 tff(352,plain,
% 18.25/18.47 (((~g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)) | (~g_false(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(353,plain,
% 18.25/18.47 (~g_false(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[352, 351])).
% 18.25/18.47 tff(354,plain,
% 18.25/18.47 (((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)) | g_false(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(355,plain,
% 18.25/18.47 ((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[354, 353])).
% 18.25/18.47 tff(356,plain,
% 18.25/18.47 ((((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)) <=> g_false_only(tptp_fun_C_1(A!6), A!6)) | (~((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6))) | (~g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(357,plain,
% 18.25/18.47 ((((~g_false(tptp_fun_C_1(A!6), A!6)) | g_true(tptp_fun_C_1(A!6), A!6)) <=> g_false_only(tptp_fun_C_1(A!6), A!6)) | (~g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[356, 355])).
% 18.25/18.47 tff(358,plain,
% 18.25/18.47 (~g_false_only(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(unit_resolution,[status(thm)],[357, 344])).
% 18.25/18.47 tff(359,plain,
% 18.25/18.47 (((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6))) | g_false_only(tptp_fun_C_1(A!6), A!6)),
% 18.25/18.47 inference(tautology,[status(thm)],[])).
% 18.25/18.47 tff(360,plain,
% 18.25/18.47 ((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.31/18.47 inference(unit_resolution,[status(thm)],[359, 358])).
% 18.31/18.47 tff(361,plain,
% 18.31/18.47 (((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))))))) <=> ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(362,plain,
% 18.31/18.47 ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | ((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))))))),
% 18.31/18.47 inference(quant_inst,[status(thm)],[])).
% 18.31/18.47 tff(363,plain,
% 18.31/18.47 ((~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) | (~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C)))))),
% 18.31/18.47 inference(modus_ponens,[status(thm)],[362, 361])).
% 18.31/18.47 tff(364,plain,
% 18.31/18.47 ((~((~g_true_only(tptp_fun_C_1(tptp_fun_C_1(A!6)), tptp_fun_C_1(A!6))) | (~g_true_only(tptp_fun_C_1(A!6), tptp_fun_C_1(tptp_fun_C_1(A!6)))) | (~g_false_only(tptp_fun_C_1(A!6), A!6)))) | (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C)))))),
% 18.31/18.47 inference(unit_resolution,[status(thm)],[363, 295])).
% 18.31/18.47 tff(365,plain,
% 18.31/18.47 (~((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))))),
% 18.31/18.47 inference(unit_resolution,[status(thm)],[364, 360])).
% 18.31/18.47 tff(366,plain,
% 18.31/18.47 (((~g_true_only(tptp_fun_C_1(A!6), A!6)) | (~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C)))) | ![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))),
% 18.31/18.47 inference(tautology,[status(thm)],[])).
% 18.31/18.47 tff(367,plain,
% 18.31/18.47 (![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))),
% 18.31/18.47 inference(unit_resolution,[status(thm)],[366, 365])).
% 18.31/18.47 tff(368,plain,
% 18.31/18.47 (((~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))) | (g_false_only(A!6, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), A!6))) <=> ((~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))) | g_false_only(A!6, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(369,plain,
% 18.31/18.47 ((~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))) | (g_false_only(A!6, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), A!6))),
% 18.31/18.47 inference(quant_inst,[status(thm)],[])).
% 18.31/18.47 tff(370,plain,
% 18.31/18.47 ((~![C: $i] : (g_false_only(C, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), C))) | g_false_only(A!6, tptp_fun_C_1(A!6)) | g_false_only(tptp_fun_C_1(A!6), A!6)),
% 18.31/18.47 inference(modus_ponens,[status(thm)],[369, 368])).
% 18.31/18.47 tff(371,plain,
% 18.31/18.47 ($false),
% 18.31/18.47 inference(unit_resolution,[status(thm)],[370, 358, 367, 342])).
% 18.31/18.47 tff(372,plain,(~![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))), inference(lemma,lemma(discharge,[]))).
% 18.31/18.47 tff(373,plain,
% 18.31/18.47 ((![A: $i] : ((~((~g_both(tptp_fun_B_3(A), A)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))))))) | ![B: $i] : ((~g_both(B, A)) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B)))))) | (~((~g_true_only(tptp_fun_B_3(A), A)) | (~((~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))))))) | (~((~g_false_only(tptp_fun_B_3(A), A)) | (~((~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))))) | ![B: $i] : ((~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))))) <=> (![A: $i] : ((~((~g_both(tptp_fun_B_3(A), A)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))))))) | (~((~g_true_only(tptp_fun_B_3(A), A)) | (~((~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))))))) | (~((~g_false_only(tptp_fun_B_3(A), A)) | (~((~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)))))) | ![B: $i] : ((~g_both(B, A)) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))))) | ![B: $i] : ((~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))) | (~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(374,plain,
% 18.31/18.47 ((![A: $i] : ((~((~g_both(tptp_fun_B_3(A), A)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))))))) | ![B: $i] : ((~g_both(B, A)) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B)))))) | (~((~g_true_only(tptp_fun_B_3(A), A)) | (~((~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))))))) | (~((~g_false_only(tptp_fun_B_3(A), A)) | (~((~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))))) | ![B: $i] : ((~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6)))))) <=> (![A: $i] : ((~((~g_both(tptp_fun_B_3(A), A)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))))))) | ![B: $i] : ((~g_both(B, A)) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B)))))) | (~((~g_true_only(tptp_fun_B_3(A), A)) | (~((~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))))))) | (~((~g_false_only(tptp_fun_B_3(A), A)) | (~((~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))))) | ![B: $i] : ((~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(375,plain,
% 18.31/18.47 ((![A: $i] : ((g_both(tptp_fun_B_3(A), A) & (![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | ![B: $i] : ((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (~g_both(B, A))) | (g_true_only(tptp_fun_B_3(A), A) & ((g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))) | ((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))))) | (g_false_only(tptp_fun_B_3(A), A) & (((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))) | ![B: $i] : ((g_true_only(B, A!6) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))) | (g_false_only(B, A!6) & g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)))) <=> (![A: $i] : ((~((~g_both(tptp_fun_B_3(A), A)) | (~(![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))))))) | ![B: $i] : ((~g_both(B, A)) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C) | (~(g_both(C, B) | g_both(B, C)))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B)))))) | (~((~g_true_only(tptp_fun_B_3(A), A)) | (~((~((~g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A))) | (~g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))))))) | (~((~g_false_only(tptp_fun_B_3(A), A)) | (~((~(g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A)) | g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)) | (~(g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A)))) | (~![C: $i] : ((~g_true_only(tptp_fun_B_3(A), C)) | (~g_true_only(C, tptp_fun_B_3(A))))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))))) | ![B: $i] : ((~((~g_true_only(B, A!6)) | (~![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))) | (~((~g_true_only(tptp_fun_C_1(B), B)) | (~g_true_only(B, tptp_fun_C_1(B))) | (~g_false_only(B, A!6))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(376,plain,
% 18.31/18.47 ((![A: $i] : (![B: $i] : ((~g_both(B, A)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) | ((g_true_only(tptp_fun_B_3(A), A) & ((((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))) | (g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (g_both(tptp_fun_B_3(A), A) & (![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | (g_false_only(tptp_fun_B_3(A), A) & ((((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A)))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)))))) | ![B: $i] : ((g_false_only(B, A!6) & (g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))) | (g_true_only(B, A!6) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))) <=> (![A: $i] : ((g_both(tptp_fun_B_3(A), A) & (![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C)) | (g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))))) | ![B: $i] : ((g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B)) | ![C: $i] : (~((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B)))) | (~g_both(B, A))) | (g_true_only(tptp_fun_B_3(A), A) & ((g_true_only(tptp_fun_B_3(A), tptp_fun_C_5(A)) & g_true_only(tptp_fun_C_5(A), tptp_fun_B_3(A))) | ((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))))) | (g_false_only(tptp_fun_B_3(A), A) & (((g_both(tptp_fun_C_4(A), tptp_fun_B_3(A)) | g_both(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_B_3(A), tptp_fun_C_4(A))) & (~g_false_only(tptp_fun_C_4(A), tptp_fun_B_3(A))) & ![C: $i] : (~(g_true_only(tptp_fun_B_3(A), C) & g_true_only(C, tptp_fun_B_3(A))))) | ![C: $i] : (g_false_only(C, tptp_fun_B_3(A)) | g_false_only(tptp_fun_B_3(A), C))))) | ![B: $i] : ((g_true_only(B, A!6) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))) | (g_false_only(B, A!6) & g_true_only(B, tptp_fun_C_1(B)) & g_true_only(tptp_fun_C_1(B), B))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(377,plain,
% 18.31/18.47 ((?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))) <=> (?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(378,plain,
% 18.31/18.47 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))))),
% 18.31/18.47 inference(monotonicity,[status(thm)],[377])).
% 18.31/18.47 tff(379,plain,
% 18.31/18.47 ((~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))))),
% 18.31/18.47 inference(rewrite,[status(thm)],[])).
% 18.31/18.47 tff(380,plain,
% 18.31/18.47 ((~(?[A: $i] : (?[B: $i] : ((g_both(B, A) & ?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B)))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & ![C: $i] : (g_false_only(B, C) | g_false_only(C, B))) | (g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))) <=> (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C)))))))),
% 18.31/18.48 inference(rewrite,[status(thm)],[])).
% 18.31/18.48 tff(381,plain,
% 18.31/18.48 (~(?[A: $i] : (?[B: $i] : ((g_both(B, A) & ?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B)))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : (((g_true_only(B, A) & ((?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))) | (g_false_only(B, A) & (![C: $i] : (g_false_only(B, C) | g_false_only(C, B)) | (?[C: $i] : (((g_both(B, C) | g_both(C, B)) & (~g_false_only(B, C))) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))))) & (~?[A: $i] : ![B: $i] : ((g_true_only(B, A) & ![C: $i] : (g_false_only(B, C) | g_false_only(C, B))) | (g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))))))),
% 18.31/18.48 inference(or_elim,[status(thm)],[25])).
% 18.31/18.48 tff(382,plain,
% 18.31/18.48 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.31/18.48 inference(modus_ponens,[status(thm)],[381, 380])).
% 18.31/18.48 tff(383,plain,
% 18.31/18.48 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.31/18.48 inference(modus_ponens,[status(thm)],[382, 378])).
% 18.31/18.48 tff(384,plain,
% 18.31/18.48 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.31/18.49 inference(modus_ponens,[status(thm)],[383, 379])).
% 18.31/18.49 tff(385,plain,
% 18.31/18.49 (~(?[A: $i] : (?[B: $i] : (g_both(B, A) & ?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) & (~?[B: $i] : ((g_true_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_both(B, A) & (![C: $i] : (g_false_only(C, B) | g_false_only(B, C)) | ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | (g_false_only(B, A) & ((?[C: $i] : ((g_both(C, B) | g_both(B, C)) & (~g_false_only(B, C)) & (~g_false_only(C, B))) & (~?[C: $i] : (g_true_only(B, C) & g_true_only(C, B)))) | ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))) & (~?[A: $i] : ![B: $i] : ((g_false_only(B, A) & ?[C: $i] : (g_true_only(B, C) & g_true_only(C, B))) | (g_true_only(B, A) & ![C: $i] : (g_false_only(C, B) | g_false_only(B, C))))))),
% 18.31/18.49 inference(modus_ponens,[status(thm)],[384, 378])).
% 18.31/18.49 unexpected number of arguments: (let ((a!1 (lambda ((A $i))
% 18.31/18.49 (let ((a!1 (lambda ((B $i))
% 18.31/18.49 (let ((a!1 (refl (~ (not (g_both B A))
% 18.31/18.49 (not (g_both B A)))))
% 18.31/18.49 (a!2 (lambda ((C $i))
% 18.31/18.49 (let ((a!1 (and (or (g_both C B)
% 18.31/18.49 (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (refl (~ (not a!1) (not a!1))))))
% 18.31/18.49 (a!3 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C B) (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (a!4 (forall ((C $i))
% 18.31/18.49 (let ((a!1 (and (or (g_both C B)
% 18.31/18.49 (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (not a!1))))
% 18.31/18.49 (a!5 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B)))))
% 18.31/18.49 (let ((a!6 (~ a!5
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))
% 18.31/18.49 (a!7 (~ (not (not a!5))
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))
% 18.31/18.49 (a!8 (or (not (g_both B A))
% 18.31/18.49 a!4
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B)))))
% 18.31/18.49 (let ((a!9 (~ (not (and (g_both B A) a!3 (not a!5)))
% 18.31/18.49 a!8)))
% 18.31/18.49 (nnf-neg a!1
% 18.31/18.49 (nnf-neg (proof-bind a!2)
% 18.31/18.49 (~ (not a!3) a!4))
% 18.31/18.49 (nnf-neg (sk a!6) a!7)
% 18.31/18.49 a!9))))))
% 18.31/18.49 (a!2 (exists ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C B) (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (a!2 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B)))))
% 18.31/18.49 (and (g_both B A) a!1 (not a!2)))))
% 18.31/18.49 (a!3 (forall ((B $i))
% 18.31/18.49 (let ((a!1 (forall ((C $i))
% 18.31/18.49 (let ((a!1 (and (or (g_both C B)
% 18.31/18.49 (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (not a!1)))))
% 18.31/18.49 (or (not (g_both B A))
% 18.31/18.49 a!1
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))))
% 18.31/18.49 (a!4 (exists ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C B) (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (a!2 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B))))
% 18.31/18.49 (a!4 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B)
% 18.31/18.49 (g_false_only B C)))))
% 18.31/18.49 (let ((a!3 (and (g_true_only B A)
% 18.31/18.49 (or (and a!1 (not a!2)) a!2)))
% 18.31/18.49 (a!5 (and (g_false_only B A)
% 18.31/18.49 (or (and a!1 (not a!2)) a!4))))
% 18.31/18.49 (or a!3 (and (g_both B A) (or a!4 a!2)) a!5)))))
% 18.31/18.49 (a!5 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C (B!3 A)) (g_both (B!3 A) C))
% 18.31/18.49 (not (g_false_only (B!3 A) C))
% 18.31/18.49 (not (g_false_only C (B!3 A))))))
% 18.31/18.49 (a!6 (exists ((C $i))
% 18.31/18.49 (and (g_true_only (B!3 A) C) (g_true_only C (B!3 A)))))
% 18.31/18.49 (a!8 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C (B!3 A)) (g_false_only (B!3 A) C))))
% 18.31/18.49 (a!11 (refl (~ (g_true_only (B!3 A) A)
% 18.31/18.49 (g_true_only (B!3 A) A))))
% 18.31/18.49 (a!12 (and (or (g_both (C!4 A) (B!3 A))
% 18.31/18.49 (g_both (B!3 A) (C!4 A)))
% 18.31/18.49 (not (g_false_only (B!3 A) (C!4 A)))
% 18.31/18.49 (not (g_false_only (C!4 A) (B!3 A)))))
% 18.31/18.49 (a!13 (proof-bind (lambda ((C $i))
% 18.31/18.49 (let ((a!1 (not (and (g_true_only (B!3 A)
% 18.31/18.49 C)
% 18.31/18.49 (g_true_only C
% 18.31/18.49 (B!3 A))))))
% 18.31/18.49 (refl (~ a!1 a!1))))))
% 18.31/18.49 (a!14 (forall ((C $i))
% 18.31/18.49 (not (and (g_true_only (B!3 A) C)
% 18.31/18.49 (g_true_only C (B!3 A))))))
% 18.31/18.49 (a!16 (and (g_true_only (B!3 A) (C!5 A))
% 18.31/18.49 (g_true_only (C!5 A) (B!3 A))))
% 18.31/18.49 (a!20 (refl (~ (g_both (B!3 A) A) (g_both (B!3 A) A))))
% 18.31/18.49 (a!24 (refl (~ (g_false_only (B!3 A) A)
% 18.31/18.49 (g_false_only (B!3 A) A)))))
% 18.31/18.49 (let ((a!7 (and (g_true_only (B!3 A) A)
% 18.31/18.49 (or (and a!5 (not a!6)) a!6)))
% 18.31/18.49 (a!9 (and (g_false_only (B!3 A) A)
% 18.31/18.49 (or (and a!5 (not a!6)) a!8)))
% 18.31/18.49 (a!15 (monotonicity (sk (~ a!5 a!12))
% 18.31/18.49 (nnf-neg a!13 (~ (not a!6) a!14))
% 18.31/18.49 (~ (and a!5 (not a!6)) (and a!12 a!14))))
% 18.31/18.49 (a!17 (~ (or (and a!5 (not a!6)) a!6)
% 18.31/18.49 (or (and a!12 a!14) a!16)))
% 18.31/18.49 (a!18 (and (g_true_only (B!3 A) A) (or (and a!12 a!14) a!16)))
% 18.31/18.49 (a!21 (nnf-pos (proof-bind (lambda ((C $i))
% 18.31/18.49 (let ((a!1 (~ (or (g_false_only C
% 18.31/18.49 (B!3 A))
% 18.31/18.49 (g_false_only (B!3 A)
% 18.31/18.49 C))
% 18.31/18.49 (or (g_false_only C
% 18.31/18.49 (B!3 A))
% 18.31/18.49 (g_false_only (B!3 A)
% 18.31/18.49 C)))))
% 18.31/18.49 (refl a!1))))
% 18.31/18.49 (~ a!8 a!8)))
% 18.31/18.49 (a!22 (~ (and (g_both (B!3 A) A) (or a!8 a!6))
% 18.31/18.49 (and (g_both (B!3 A) A) (or a!8 a!16))))
% 18.31/18.49 (a!25 (~ (or (and a!5 (not a!6)) a!8)
% 18.31/18.49 (or (and a!12 a!14) a!8)))
% 18.31/18.49 (a!26 (and (g_false_only (B!3 A) A) (or (and a!12 a!14) a!8))))
% 18.31/18.49 (let ((a!10 (or a!7 (and (g_both (B!3 A) A) (or a!8 a!6)) a!9))
% 18.31/18.49 (a!19 (monotonicity a!11
% 18.31/18.49 (monotonicity a!15
% 18.31/18.49 (sk (~ a!6 a!16))
% 18.31/18.49 a!17)
% 18.31/18.49 (~ a!7 a!18)))
% 18.31/18.49 (a!23 (monotonicity a!20
% 18.31/18.49 (monotonicity a!21
% 18.31/18.49 (sk (~ a!6 a!16))
% 18.31/18.49 (~ (or a!8 a!6)
% 18.31/18.49 (or a!8 a!16)))
% 18.31/18.49 a!22))
% 18.31/18.49 (a!27 (or a!18 (and (g_both (B!3 A) A) (or a!8 a!16)) a!26)))
% 18.31/18.49 (let ((a!28 (trans (sk (~ a!4 a!10))
% 18.31/18.49 (monotonicity a!19
% 18.31/18.49 a!23
% 18.31/18.49 (monotonicity a!24
% 18.31/18.49 (monotonicity a!15
% 18.31/18.49 a!21
% 18.31/18.49 a!25)
% 18.31/18.49 (~ a!9 a!26))
% 18.31/18.49 (~ a!10 a!27))
% 18.31/18.49 (~ a!4 a!27)))
% 18.31/18.49 (a!30 (~ (not (and a!2 (not a!4))) (or a!3 a!27))))
% 18.31/18.49 (let ((a!29 (nnf-neg a!28 (~ (not (not a!4)) a!27))))
% 18.31/18.49 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3)) a!29 a!30))))))))
% 18.31/18.49 (a!2 (exists ((A $i))
% 18.31/18.49 (let ((a!1 (exists ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C B) (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (a!2 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B)))))
% 18.31/18.49 (and (g_both B A) a!1 (not a!2)))))
% 18.31/18.49 (a!2 (exists ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (or (g_both C B) (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (a!2 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B))))
% 18.31/18.49 (a!4 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B)
% 18.31/18.49 (g_false_only B C)))))
% 18.31/18.49 (let ((a!3 (and (g_true_only B A)
% 18.31/18.49 (or (and a!1 (not a!2)) a!2)))
% 18.31/18.49 (a!5 (and (g_false_only B A)
% 18.31/18.49 (or (and a!1 (not a!2)) a!4))))
% 18.31/18.49 (or a!3 (and (g_both B A) (or a!4 a!2)) a!5))))))
% 18.31/18.49 (and a!1 (not a!2)))))
% 18.31/18.49 (a!3 (forall ((A $i))
% 18.31/18.49 (let ((a!1 (forall ((B $i))
% 18.31/18.49 (let ((a!1 (forall ((C $i))
% 18.31/18.49 (let ((a!1 (and (or (g_both C B)
% 18.31/18.49 (g_both B C))
% 18.31/18.49 (not (g_false_only B C))
% 18.31/18.49 (not (g_false_only C B)))))
% 18.31/18.49 (not a!1)))))
% 18.31/18.49 (or (not (g_both B A))
% 18.31/18.49 a!1
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))))
% 18.31/18.49 (a!2 (and (or (g_both (C!4 A) (B!3 A))
% 18.31/18.49 (g_both (B!3 A) (C!4 A)))
% 18.31/18.49 (not (g_false_only (B!3 A) (C!4 A)))
% 18.31/18.49 (not (g_false_only (C!4 A) (B!3 A)))))
% 18.31/18.49 (a!3 (forall ((C $i))
% 18.31/18.49 (not (and (g_true_only (B!3 A) C)
% 18.31/18.49 (g_true_only C (B!3 A))))))
% 18.31/18.49 (a!4 (and (g_true_only (B!3 A) (C!5 A))
% 18.31/18.49 (g_true_only (C!5 A) (B!3 A))))
% 18.31/18.49 (a!6 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C (B!3 A)) (g_false_only (B!3 A) C)))))
% 18.31/18.49 (let ((a!5 (and (g_true_only (B!3 A) A) (or (and a!2 a!3) a!4)))
% 18.31/18.49 (a!7 (and (g_false_only (B!3 A) A) (or (and a!2 a!3) a!6))))
% 18.31/18.49 (let ((a!8 (or a!5 (and (g_both (B!3 A) A) (or a!6 a!4)) a!7)))
% 18.31/18.49 (or a!1 a!8))))))
% 18.31/18.49 (a!4 (exists ((A $i))
% 18.31/18.49 (forall ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B))))
% 18.31/18.49 (a!2 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B) (g_false_only B C)))))
% 18.31/18.49 (or (and (g_false_only B A) a!1) (and (g_true_only B A) a!2))))))
% 18.31/18.49 (a!5 (forall ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C) (g_true_only C B))))
% 18.31/18.49 (a!2 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B) (g_false_only B C)))))
% 18.31/18.49 (or (and (g_false_only B A!6) a!1) (and (g_true_only B A!6) a!2)))))
% 18.31/18.49 (a!6 (forall ((B $i))
% 18.31/18.49 (let ((a!1 (and (g_false_only B A!6)
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))
% 18.31/18.49 (a!2 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B) (g_false_only B C)))))
% 18.31/18.49 (or a!1 (and (g_true_only B A!6) a!2))))))
% 18.31/18.49 (let ((a!7 (nnf-pos (proof-bind (lambda ((B $i))
% 18.31/18.49 (let ((a!1 (exists ((C $i))
% 18.31/18.49 (and (g_true_only B C)
% 18.31/18.49 (g_true_only C B))))
% 18.31/18.49 (a!3 (and (g_false_only B A!6)
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))
% 18.31/18.49 (a!5 (lambda ((C $i))
% 18.31/18.49 (refl (~ (or (g_false_only C B)
% 18.31/18.49 (g_false_only B C))
% 18.31/18.49 (or (g_false_only C B)
% 18.31/18.49 (g_false_only B C))))))
% 18.31/18.49 (a!6 (forall ((C $i))
% 18.31/18.49 (or (g_false_only C B)
% 18.31/18.49 (g_false_only B C)))))
% 18.31/18.49 (let ((a!2 (~ a!1
% 18.31/18.49 (and (g_true_only B (C!1 B))
% 18.31/18.49 (g_true_only (C!1 B) B))))
% 18.31/18.49 (a!7 (monotonicity (refl (~ (g_true_only B
% 18.31/18.49 A!6)
% 18.31/18.49 (g_true_only B
% 18.31/18.49 A!6)))
% 18.31/18.49 (nnf-pos (proof-bind a!5)
% 18.31/18.49 (~ a!6 a!6))
% 18.31/18.49 (~ (and (g_true_only B
% 18.31/18.49 A!6)
% 18.31/18.49 a!6)
% 18.31/18.49 (and (g_true_only B
% 18.31/18.49 A!6)
% 18.31/18.49 a!6))))
% 18.31/18.49 (a!8 (or (and (g_false_only B A!6) a!1)
% 18.31/18.49 (and (g_true_only B A!6) a!6))))
% 18.31/18.49 (let ((a!4 (monotonicity (refl (~ (g_false_only B
% 18.31/18.49 A!6)
% 18.31/18.49 (g_false_only B
% 18.31/18.49 A!6)))
% 18.31/18.49 (sk a!2)
% 18.31/18.49 (~ (and (g_false_only B
% 18.31/18.49 A!6)
% 18.31/18.49 a!1)
% 18.31/18.49 a!3)))
% 18.31/18.49 (a!9 (~ a!8
% 18.31/18.49 (or a!3
% 18.31/18.49 (and (g_true_only B A!6)
% 18.31/18.49 a!6)))))
% 18.31/18.49 (monotonicity a!4 a!7 a!9))))))
% 18.31/18.49 (~ a!5 a!6)))
% 18.31/18.49 (a!9 (~ (not (and a!2 (not a!4))) (or a!3 a!6))))
% 18.31/18.49 (let ((a!8 (nnf-neg (trans (sk (~ a!4 a!5)) a!7 (~ a!4 a!6))
% 18.31/18.49 (~ (not (not a!4)) a!6))))
% 18.31/18.49 (nnf-neg (nnf-neg (proof-bind a!1) (~ (not a!2) a!3)) a!8 a!9))))
% 18.31/18.49 Proof display could not be completed: unexpected number of arguments
% 18.31/18.50 % E exiting
%------------------------------------------------------------------------------