%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU104+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:54 AM UTC 2025
% Result : Theorem 0.82s 0.98s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU104+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 06:05:11 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.82/0.98 % SZS status Theorem
% 0.82/0.98 % SZS output start Proof
% 0.82/0.98 tff(in_type, type, (
% 0.82/0.98 in: ( $i * $i ) > $o)).
% 0.82/0.98 tff(tptp_fun_A_11_type, type, (
% 0.82/0.98 tptp_fun_A_11: $i)).
% 0.82/0.98 tff(symmetric_difference_type, type, (
% 0.82/0.98 symmetric_difference: ( $i * $i ) > $i)).
% 0.82/0.98 tff(set_difference_type, type, (
% 0.82/0.98 set_difference: ( $i * $i ) > $i)).
% 0.82/0.98 tff(tptp_fun_C_9_type, type, (
% 0.82/0.98 tptp_fun_C_9: $i > $i)).
% 0.82/0.98 tff(tptp_fun_B_10_type, type, (
% 0.82/0.98 tptp_fun_B_10: $i > $i)).
% 0.82/0.98 tff(set_union2_type, type, (
% 0.82/0.98 set_union2: ( $i * $i ) > $i)).
% 0.82/0.98 tff(preboolean_type, type, (
% 0.82/0.98 preboolean: $i > $o)).
% 0.82/0.98 tff(element_type, type, (
% 0.82/0.98 element: ( $i * $i ) > $o)).
% 0.82/0.98 tff(empty_type, type, (
% 0.82/0.98 empty: $i > $o)).
% 0.82/0.98 tff(1,plain,
% 0.82/0.98 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(2,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[1])).
% 0.82/0.98 tff(3,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.82/0.98 tff(5,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.82/0.98 tff(6,plain,(
% 0.82/0.98 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.82/0.98 inference(skolemize,[status(sab)],[5])).
% 0.82/0.98 tff(7,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.82/0.98 tff(8,plain,
% 0.82/0.98 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(9,plain,
% 0.82/0.98 (set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)) = set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.82/0.98 tff(10,plain,
% 0.82/0.98 (set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)) = set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 0.82/0.98 inference(symmetry,[status(thm)],[9])).
% 0.82/0.98 tff(11,plain,
% 0.82/0.98 (^[A: $i, B: $i] : refl((set_union2(A, B) = symmetric_difference(A, set_difference(B, A))) <=> (set_union2(A, B) = symmetric_difference(A, set_difference(B, A))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(12,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A))) <=> ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[11])).
% 0.82/0.98 tff(13,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A))) <=> ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))),
% 0.82/0.98 inference(rewrite,[status(thm)],[])).
% 0.82/0.98 tff(14,axiom,(![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t98_xboole_1')).
% 0.82/0.98 tff(15,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.82/0.98 tff(16,plain,(
% 0.82/0.98 ![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))),
% 0.82/0.98 inference(skolemize,[status(sab)],[15])).
% 0.82/0.98 tff(17,plain,
% 0.82/0.98 (![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))),
% 0.82/0.98 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.82/0.98 tff(18,plain,
% 0.82/0.98 ((~![A: $i, B: $i] : (set_union2(A, B) = symmetric_difference(A, set_difference(B, A)))) | (set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)) = symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))))),
% 0.82/0.98 inference(quant_inst,[status(thm)],[])).
% 0.82/0.98 tff(19,plain,
% 0.82/0.98 (set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11)) = symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)))),
% 0.82/0.98 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.82/0.98 tff(20,plain,
% 0.82/0.98 (symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))) = set_union2(tptp_fun_C_9(A!11), tptp_fun_B_10(A!11))),
% 0.82/0.98 inference(symmetry,[status(thm)],[19])).
% 0.82/0.98 tff(21,plain,
% 0.82/0.98 (symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))) = set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))),
% 0.82/0.98 inference(transitivity,[status(thm)],[20, 10])).
% 0.82/0.98 tff(22,plain,
% 0.82/0.98 (in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11) <=> in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.98 inference(monotonicity,[status(thm)],[21])).
% 0.82/0.98 tff(23,plain,
% 0.82/0.98 (in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11) <=> in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 0.82/0.98 inference(symmetry,[status(thm)],[22])).
% 0.82/0.98 tff(24,plain,
% 0.82/0.98 ((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) <=> (~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11))),
% 0.82/0.98 inference(monotonicity,[status(thm)],[23])).
% 0.82/0.98 tff(25,plain,
% 0.82/0.98 (^[A: $i] : refl((~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(26,plain,
% 0.82/0.98 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[25])).
% 0.82/0.98 tff(27,plain,
% 0.82/0.98 (^[A: $i] : rewrite((~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(28,plain,
% 0.82/0.98 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.98 inference(quant_intro,[status(thm)],[27])).
% 0.82/0.98 tff(29,plain,
% 0.82/0.98 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.98 inference(transitivity,[status(thm)],[28, 26])).
% 0.82/0.98 tff(30,plain,
% 0.82/0.98 (^[A: $i] : trans(monotonicity(rewrite(((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))), rewrite((preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))) <=> (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))), ((((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> (((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A)))))) & (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))))), rewrite((((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A)))))) & (preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))), ((((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))))),
% 0.82/0.98 inference(bind,[status(th)],[])).
% 0.82/0.98 tff(31,plain,
% 0.82/0.98 (![A: $i] : (((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)))))) <=> ![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[30])).
% 0.82/0.99 tff(32,plain,
% 0.82/0.99 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(33,plain,
% 0.82/0.99 (^[A: $i] : rewrite((preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(34,plain,
% 0.82/0.99 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) <=> ![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[33])).
% 0.82/0.99 tff(35,axiom,(![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((in(B, A) & in(C, A)) => (in(set_union2(B, C), A) & in(set_difference(B, C), A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_finsub_1')).
% 0.82/0.99 tff(36,plain,
% 0.82/0.99 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.82/0.99 tff(37,plain,
% 0.82/0.99 (![A: $i] : (preboolean(A) <=> ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.82/0.99 tff(38,plain,(
% 0.82/0.99 ![A: $i] : (((~preboolean(A)) | ![B: $i, C: $i] : ((~(in(B, A) & in(C, A))) | (in(set_union2(B, C), A) & in(set_difference(B, C), A)))) & (preboolean(A) | (~((~(in(tptp_fun_B_10(A), A) & in(tptp_fun_C_9(A), A))) | (in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A) & in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))),
% 0.82/0.99 inference(skolemize,[status(sab)],[37])).
% 0.82/0.99 tff(39,plain,
% 0.82/0.99 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.82/0.99 tff(40,plain,
% 0.82/0.99 (![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.82/0.99 tff(41,plain,
% 0.82/0.99 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(42,plain,
% 0.82/0.99 ((~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))) <=> (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(43,plain,
% 0.82/0.99 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[42])).
% 0.82/0.99 tff(44,plain,
% 0.82/0.99 (((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))) <=> ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[43, 41])).
% 0.82/0.99 tff(45,plain,
% 0.82/0.99 ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_union2(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(46,plain,
% 0.82/0.99 ((~![A: $i] : (~((~((~preboolean(A)) | ![B: $i, C: $i] : ((~in(B, A)) | (~in(C, A)) | (~((~in(set_union2(B, C), A)) | (~in(set_difference(B, C), A))))))) | (~(preboolean(A) | (~((~in(tptp_fun_B_10(A), A)) | (~in(tptp_fun_C_9(A), A)) | (~((~in(set_union2(tptp_fun_B_10(A), tptp_fun_C_9(A)), A)) | (~in(set_difference(tptp_fun_B_10(A), tptp_fun_C_9(A)), A))))))))))) | (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.82/0.99 tff(47,plain,
% 0.82/0.99 (~((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[46, 40])).
% 0.82/0.99 tff(48,plain,
% 0.82/0.99 (((~((~preboolean(A!11)) | ![B: $i, C: $i] : ((~in(B, A!11)) | (~in(C, A!11)) | (~((~in(set_difference(B, C), A!11)) | (~in(set_union2(B, C), A!11))))))) | (~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))))) | (preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(49,plain,
% 0.82/0.99 (preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.82/0.99 tff(50,plain,
% 0.82/0.99 (((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11))))) <=> ((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11)))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(51,plain,
% 0.82/0.99 ((~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A))))))) <=> (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A)))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(52,plain,
% 0.82/0.99 ((~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A)))) => preboolean(A)))) <=> (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A)))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(53,axiom,(~![A: $i] : ((~empty(A)) => (![B: $i] : (element(B, A) => ![C: $i] : (element(C, A) => (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A)))) => preboolean(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_finsub_1')).
% 0.82/0.99 tff(54,plain,
% 0.82/0.99 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.82/0.99 tff(55,plain,
% 0.82/0.99 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.82/0.99 tff(56,plain,
% 0.82/0.99 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.82/0.99 tff(57,plain,
% 0.82/0.99 (~![A: $i] : (empty(A) | preboolean(A) | (~![B: $i] : ((~element(B, A)) | ![C: $i] : ((~element(C, A)) | (in(symmetric_difference(B, C), A) & in(set_difference(B, C), A))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.82/0.99 tff(58,plain,
% 0.82/0.99 ((~empty(A!11)) & (~preboolean(A!11)) & ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.82/0.99 tff(59,plain,
% 0.82/0.99 (~preboolean(A!11)),
% 0.82/0.99 inference(and_elim,[status(thm)],[58])).
% 0.82/0.99 tff(60,plain,
% 0.82/0.99 ((~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))) | preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(61,plain,
% 0.82/0.99 ((~(preboolean(A!11) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))))) | (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.82/0.99 tff(62,plain,
% 0.82/0.99 (~((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[61, 49])).
% 0.82/0.99 tff(63,plain,
% 0.82/0.99 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(64,plain,
% 0.82/0.99 ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.82/0.99 tff(65,plain,
% 0.82/0.99 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | in(tptp_fun_B_10(A!11), A!11)),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(66,plain,
% 0.82/0.99 (in(tptp_fun_B_10(A!11), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.82/0.99 tff(67,plain,
% 0.82/0.99 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(68,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[67])).
% 0.82/0.99 tff(69,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(70,plain,
% 0.82/0.99 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(71,plain,
% 0.82/0.99 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[70])).
% 0.82/0.99 tff(72,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.82/0.99 tff(73,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.82/0.99 tff(74,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.82/0.99 tff(75,plain,(
% 0.82/0.99 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(skolemize,[status(sab)],[74])).
% 0.82/0.99 tff(76,plain,
% 0.82/0.99 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.82/0.99 tff(77,plain,
% 0.82/0.99 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(78,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(79,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_B_10(A!11), A!11)) | element(tptp_fun_B_10(A!11), A!11)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.82/0.99 tff(80,plain,
% 0.82/0.99 (element(tptp_fun_B_10(A!11), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[79, 76, 66])).
% 0.82/0.99 tff(81,plain,
% 0.82/0.99 (^[B: $i] : refl(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(82,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[81])).
% 0.82/0.99 tff(83,plain,
% 0.82/0.99 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(84,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[83])).
% 0.82/0.99 tff(85,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[84, 82])).
% 0.82/0.99 tff(86,plain,
% 0.82/0.99 (^[B: $i] : rewrite(((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11)))) <=> ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11)))))))),
% 0.82/0.99 inference(bind,[status(th)],[])).
% 0.82/0.99 tff(87,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11)))) <=> ![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(quant_intro,[status(thm)],[86])).
% 0.82/0.99 tff(88,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (in(symmetric_difference(B, C), A!11) & in(set_difference(B, C), A!11))))),
% 0.82/0.99 inference(and_elim,[status(thm)],[58])).
% 0.82/0.99 tff(89,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.82/0.99 tff(90,plain,
% 0.82/0.99 (![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.82/0.99 tff(91,plain,
% 0.82/0.99 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11))))))) <=> ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11))))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(92,plain,
% 0.82/0.99 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | ((~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11))))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(93,plain,
% 0.82/0.99 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~element(tptp_fun_B_10(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.82/0.99 tff(94,plain,
% 0.82/0.99 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 0.82/0.99 tff(95,plain,
% 0.82/0.99 (((~in(tptp_fun_B_10(A!11), A!11)) | (~in(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) | in(tptp_fun_C_9(A!11), A!11)),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(96,plain,
% 0.82/0.99 (in(tptp_fun_C_9(A!11), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[95, 62])).
% 0.82/0.99 tff(97,plain,
% 0.82/0.99 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(98,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(99,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_9(A!11), A!11)) | element(tptp_fun_C_9(A!11), A!11)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.82/0.99 tff(100,plain,
% 0.82/0.99 (element(tptp_fun_C_9(A!11), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[99, 76, 96])).
% 0.82/0.99 tff(101,plain,
% 0.82/0.99 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(102,plain,
% 0.82/0.99 (((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))) <=> ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(103,plain,
% 0.82/0.99 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))))),
% 0.82/0.99 inference(monotonicity,[status(thm)],[102])).
% 0.82/0.99 tff(104,plain,
% 0.82/0.99 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 0.82/0.99 inference(transitivity,[status(thm)],[103, 101])).
% 0.82/0.99 tff(105,plain,
% 0.82/0.99 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(106,plain,
% 0.82/0.99 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_B_10(A!11), C), A!11)) | (~in(set_difference(tptp_fun_B_10(A!11), C), A!11)))))) | (~element(tptp_fun_C_9(A!11), A!11)) | (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))))),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.82/0.99 tff(107,plain,
% 0.82/0.99 (~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[106, 100, 94])).
% 0.82/0.99 tff(108,plain,
% 0.82/0.99 (((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(symmetric_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))) | in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(109,plain,
% 0.82/0.99 (in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.82/0.99 tff(110,plain,
% 0.82/0.99 ((~((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)))) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 0.82/0.99 inference(tautology,[status(thm)],[])).
% 0.82/0.99 tff(111,plain,
% 0.82/0.99 (~in(set_union2(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[110, 109, 64])).
% 0.82/0.99 tff(112,plain,
% 0.82/0.99 (~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[111, 24])).
% 0.82/0.99 tff(113,plain,
% 0.82/0.99 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 0.82/0.99 inference(rewrite,[status(thm)],[])).
% 0.82/0.99 tff(114,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11))),
% 0.82/0.99 inference(quant_inst,[status(thm)],[])).
% 0.82/0.99 tff(115,plain,
% 0.82/0.99 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.99 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.82/0.99 tff(116,plain,
% 0.82/0.99 (element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)),
% 0.82/0.99 inference(unit_resolution,[status(thm)],[115, 76, 109])).
% 0.82/0.99 tff(117,plain,
% 0.82/0.99 (((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11))))))) <=> ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11))))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(118,plain,
% 0.82/1.00 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | ((~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11))))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(119,plain,
% 0.82/1.00 ((~![B: $i] : ((~element(B, A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(B, C), A!11)) | (~in(set_difference(B, C), A!11))))))) | (~element(tptp_fun_C_9(A!11), A!11)) | ![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.82/1.00 tff(120,plain,
% 0.82/1.00 (![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[119, 90, 100])).
% 0.82/1.00 tff(121,plain,
% 0.82/1.00 (((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))) | ((~element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)))))) <=> ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))) | (~element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)))))),
% 0.82/1.00 inference(rewrite,[status(thm)],[])).
% 0.82/1.00 tff(122,plain,
% 0.82/1.00 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))) | ((~element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)))))),
% 0.82/1.00 inference(quant_inst,[status(thm)],[])).
% 0.82/1.00 tff(123,plain,
% 0.82/1.00 ((~![C: $i] : ((~element(C, A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), C), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), C), A!11)))))) | (~element(set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11)), A!11)) | (~((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11))))),
% 0.82/1.00 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.82/1.00 tff(124,plain,
% 0.82/1.00 (~((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)))),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[123, 120, 116])).
% 0.82/1.00 tff(125,plain,
% 0.82/1.00 (((~in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)) | (~in(set_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11))) | in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 0.82/1.00 inference(tautology,[status(thm)],[])).
% 0.82/1.00 tff(126,plain,
% 0.82/1.00 (in(symmetric_difference(tptp_fun_C_9(A!11), set_difference(tptp_fun_B_10(A!11), tptp_fun_C_9(A!11))), A!11)),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.82/1.00 tff(127,plain,
% 0.82/1.00 ($false),
% 0.82/1.00 inference(unit_resolution,[status(thm)],[126, 112])).
% 0.82/1.00 % SZS output end Proof
% 0.82/1.00 % E exiting
%------------------------------------------------------------------------------