%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET974+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:26:44 AM UTC 2025
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET974+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 05:54:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(in_type, type, (
% 0.14/0.39 in: ( $i * $i ) > $o)).
% 0.14/0.39 tff(set_intersection2_type, type, (
% 0.14/0.39 set_intersection2: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_B_6_type, type, (
% 0.14/0.39 tptp_fun_B_6: $i)).
% 0.14/0.39 tff(tptp_fun_A_7_type, type, (
% 0.14/0.39 tptp_fun_A_7: $i)).
% 0.14/0.39 tff(disjoint_type, type, (
% 0.14/0.39 disjoint: ( $i * $i ) > $o)).
% 0.14/0.39 tff(tptp_fun_D_4_type, type, (
% 0.14/0.39 tptp_fun_D_4: $i)).
% 0.14/0.39 tff(tptp_fun_C_5_type, type, (
% 0.14/0.39 tptp_fun_C_5: $i)).
% 0.14/0.39 tff(tptp_fun_G_2_type, type, (
% 0.14/0.39 tptp_fun_G_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_C_8_type, type, (
% 0.14/0.39 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.14/0.39 tff(cartesian_product2_type, type, (
% 0.14/0.39 cartesian_product2: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_F_3_type, type, (
% 0.14/0.39 tptp_fun_F_3: ( $i * $i * $i * $i * $i ) > $i)).
% 0.14/0.39 tff(ordered_pair_type, type, (
% 0.14/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.14/0.39 tff(1,assumption,(![C: $i] : (~in(C, set_intersection2(C!5, D!4)))), introduced(assumption)).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))) <=> (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))), (((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))))), rewrite(((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))), (((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(12,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_xboole_0')).
% 0.14/0.39 tff(13,plain,
% 0.14/0.39 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.39 tff(14,plain,(
% 0.14/0.39 ![A: $i, B: $i] : ((disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B))) & (![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[13])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~(![C: $i] : (~in(C, set_intersection2(A, B))) | (~disjoint(A, B))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[16, 3])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))) | (~((~disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))) | ![C: $i] : (~in(C, set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (~((~(disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))) | (~((~disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))) | ![C: $i] : (~in(C, set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (((~(disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))) | (~((~disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))) | ![C: $i] : (~in(C, set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))))) | (disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) <=> (~(disjoint(C!5, D!4) | disjoint(A!7, B!6)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))) <=> ((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 ((~((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))) <=> (~((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : ((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(27,axiom,(~![A: $i, B: $i, C: $i, D: $i] : ((disjoint(A, B) | disjoint(C, D)) => disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t127_zfmisc_1')).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (~![A: $i, B: $i, C: $i, D: $i] : ((~(disjoint(C, D) | disjoint(A, B))) | disjoint(cartesian_product2(A, C), cartesian_product2(B, D)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.14/0.40 tff(32,plain,(
% 0.14/0.40 ~((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[31])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (~((~(disjoint(C!5, D!4) | disjoint(A!7, B!6))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (~disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))),
% 0.14/0.40 inference(or_elim,[status(thm)],[33])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 ((~(disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))) | disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 ((~(disjoint(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4))))) | in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[36, 21])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl(((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))))) <=> ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite(((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | ((A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A))) & in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D)) & in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))) <=> ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | ((A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A))) & in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D)) & in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E)))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite((~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~(((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D))) & in(G, set_intersection2(C, E)))))) <=> (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~(((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D))) & in(G, set_intersection2(C, E)))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.40 tff(45,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~(((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D))) & in(G, set_intersection2(C, E))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t104_zfmisc_1')).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (~(in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E))) & ![F: $i, G: $i] : (~((A = ordered_pair(F, G)) & in(F, set_intersection2(B, D)) & in(G, set_intersection2(C, E))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.14/0.40 tff(48,plain,(
% 0.14/0.40 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | ((A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A))) & in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D)) & in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[47])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))) | ((~in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))) | (~((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))) | (~in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))) | (~((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))) | ((~in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))) | (~((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~in(A, set_intersection2(cartesian_product2(B, C), cartesian_product2(D, E)))) | (~((~(A = ordered_pair(tptp_fun_F_3(E, D, C, B, A), tptp_fun_G_2(E, D, C, B, A)))) | (~in(tptp_fun_F_3(E, D, C, B, A), set_intersection2(B, D))) | (~in(tptp_fun_G_2(E, D, C, B, A), set_intersection2(C, E))))))) | (~in(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)), set_intersection2(cartesian_product2(A!7, C!5), cartesian_product2(B!6, D!4)))) | (~((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (~((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[53, 50, 37])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 (((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4)))) | in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(56,plain,
% 0.14/0.41 (in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.14/0.41 tff(57,plain,
% 0.14/0.41 ((~![C: $i] : (~in(C, set_intersection2(C!5, D!4)))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[57, 56, 1])).
% 0.14/0.41 tff(59,plain,(~![C: $i] : (~in(C, set_intersection2(C!5, D!4)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(60,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(C!5, D!4) | in(tptp_fun_C_8(D!4, C!5), set_intersection2(C!5, D!4)))) | (~((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4)))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (~((~(disjoint(C!5, D!4) | in(tptp_fun_C_8(D!4, C!5), set_intersection2(C!5, D!4)))) | (~((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[60, 17])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 (((~(disjoint(C!5, D!4) | in(tptp_fun_C_8(D!4, C!5), set_intersection2(C!5, D!4)))) | (~((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4)))))) | ((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 ((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 ((~((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4))))) | (~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 ((~disjoint(C!5, D!4)) | ![C: $i] : (~in(C, set_intersection2(C!5, D!4)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (~disjoint(C!5, D!4)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 (disjoint(C!5, D!4) | disjoint(A!7, B!6)),
% 0.14/0.41 inference(or_elim,[status(thm)],[33])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 (disjoint(A!7, B!6)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | in(tptp_fun_C_8(B, A), set_intersection2(A, B)))) | (~((~disjoint(A, B)) | ![C: $i] : (~in(C, set_intersection2(A, B)))))))) | (~((~(disjoint(A!7, B!6) | in(tptp_fun_C_8(B!6, A!7), set_intersection2(A!7, B!6)))) | (~((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6)))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (~((~(disjoint(A!7, B!6) | in(tptp_fun_C_8(B!6, A!7), set_intersection2(A!7, B!6)))) | (~((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[69, 17])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (((~(disjoint(A!7, B!6) | in(tptp_fun_C_8(B!6, A!7), set_intersection2(A!7, B!6)))) | (~((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6)))))) | ((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 ((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 ((~((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6))))) | (~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6)))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 ((~disjoint(A!7, B!6)) | ![C: $i] : (~in(C, set_intersection2(A!7, B!6)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 (![C: $i] : (~in(C, set_intersection2(A!7, B!6)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (((~(tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)) = ordered_pair(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5)))))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))) | (~in(tptp_fun_G_2(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(C!5, D!4)))) | in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[76, 54])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 ((~![C: $i] : (~in(C, set_intersection2(A!7, B!6)))) | (~in(tptp_fun_F_3(D!4, B!6, C!5, A!7, tptp_fun_C_8(cartesian_product2(B!6, D!4), cartesian_product2(A!7, C!5))), set_intersection2(A!7, B!6)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(79,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[78, 77, 75])).
% 0.14/0.41 % SZS output end Proof
% 0.14/0.41 % E exiting
%------------------------------------------------------------------------------