%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN354+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:38:52 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN354+1 : TPTP v9.0.0. Released v2.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:31:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_f_type, type, (
% 0.19/0.36 big_f: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_X2_0_type, type, (
% 0.19/0.36 tptp_fun_X2_0: $i)).
% 0.19/0.36 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.36 tptp_fun_X1_1: $i)).
% 0.19/0.36 tff(big_g_type, type, (
% 0.19/0.36 big_g: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_Z_2_type, type, (
% 0.19/0.36 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 0.19/0.36 tff(elem_3_type, type, (
% 0.19/0.36 elem_3: $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[Y1: $i, Y2: $i] : refl((~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2)))))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2)))))) <=> ![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (^[Y1: $i, Y2: $i] : rewrite((~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2)))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))))) <=> ![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (^[Y1: $i, Y2: $i] : rewrite((~((big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 (![Y1: $i, Y2: $i] : (~((big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)))) <=> ![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2)))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X1, X2) => (big_g(X1, X2) => (((big_g(X2, Z) <=> big_g(Y2, Z)) => (big_f(Y1, Y2) => big_f(X2, Y2))) => ((big_g(X2, Z) <=> big_g(Y1, Z)) => ((big_f(X1, Y1) & big_f(X2, Y1)) & big_f(Y1, Y2))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(9,axiom,(~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (big_f(X1, X2) => (big_g(X1, X2) => (((big_g(X2, Z) <=> big_g(Y2, Z)) => (big_f(Y1, Y2) => big_f(X2, Y2))) => ((big_g(X2, Z) <=> big_g(Y1, Z)) => ((big_f(X1, Y1) & big_f(X2, Y1)) & big_f(Y1, Y2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_20_1')).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1, Y1) & big_f(X2, Y1) & big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y1, Z))) | (~(big_f(X2, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2, Z) <=> big_g(Y2, Z))))) | (~big_g(X1, X2)) | (~big_f(X1, X2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.19/0.37 tff(14,plain,(
% 0.19/0.37 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, Z) <=> big_g(Y1, Z))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, Z) <=> big_g(Y2, Z))))) | (~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)))), ![Y1: $i, Y2: $i] : (~((big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)))))),
% 0.19/0.37 inference(transitivity,[status(sab)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (big_f(X1!1, Y1) & big_f(X2!0, Y1) & big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 ((~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~(big_f(X2!0, X2!0) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)))))) | (~((~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)) | (~big_f(X1!1, X2!0)))))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~(big_f(X2!0, X2!0) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)))))) | (~((~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)) | (~big_f(X1!1, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~(big_f(X2!0, X2!0) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)))))) | (~((~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)) | (~big_f(X1!1, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~(big_f(X2!0, X2!0) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)))))) | (~((~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)) | (~big_f(X1!1, X2!0))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[23, 17])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X1!1)) <=> big_g(X1!1, tptp_fun_Z_2(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X1!1, X1!1)) | (~big_f(X2!0, X1!1)))) | (~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)))) | ((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 ((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~(big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~(big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~(big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[29, 27])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~(big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 17])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, elem!3)) | (~big_f(X2!0, elem!3)) | (~big_f(elem!3, elem!3)))) | (~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | (~((~(big_g(X2!0, tptp_fun_Z_2(elem!3, elem!3)) <=> big_g(elem!3, tptp_fun_Z_2(elem!3, elem!3)))) | big_f(X2!0, elem!3) | (~big_f(elem!3, elem!3))))) | big_f(X1!1, X2!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (big_f(X1!1, X2!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))) | (~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((~((~big_f(X1!1, X2!0)) | big_f(X2!0, X2!0))) | big_f(X2!0, X2!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (big_f(X2!0, X2!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[37, 26])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))) | (~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[39, 35, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))))) | ((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X2!0, X2!0) | (~big_f(X2!0, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)) | (~big_f(X2!0, X2!0)))))) <=> (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X2!0, X2!0) | (~big_f(X2!0, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)) | (~big_f(X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X2!0, X2!0) | (~big_f(X2!0, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)) | (~big_f(X2!0, X2!0))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X2!0, X2!0) | (~big_f(X2!0, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)) <=> big_g(X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0)) | (~big_f(X2!0, X2!0))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((~![Y1: $i, Y2: $i] : (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y1, tptp_fun_Z_2(Y2, Y1)))) | (~(big_f(X2!0, Y2) | (~big_f(Y1, Y2)) | (~(big_g(X2!0, tptp_fun_Z_2(Y2, Y1)) <=> big_g(Y2, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X1!1, Y1)) | (~big_f(X2!0, Y1)) | (~big_f(Y1, Y2))))))) | (~((~big_g(X1!1, X2!0)) | (~big_f(X1!1, X2!0)) | (~((~big_f(X1!1, X2!0)) | (~big_f(X2!0, X2!0))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 17, 42])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------