TSTP Solution File: SEU120+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 20 07:27:33 EDT 2022
% Result : Theorem 42.21s 27.16s
% Output : Proof 42.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 09:35:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 42.21/27.16 % SZS status Theorem
% 42.21/27.16 % SZS output start Proof
% 42.21/27.16 tff(in_type, type, (
% 42.21/27.16 in: ( $i * $i ) > $o)).
% 42.21/27.16 tff(set_intersection2_type, type, (
% 42.21/27.16 set_intersection2: ( $i * $i ) > $i)).
% 42.21/27.16 tff(tptp_fun_A_6_type, type, (
% 42.21/27.16 tptp_fun_A_6: $i)).
% 42.21/27.16 tff(tptp_fun_B_5_type, type, (
% 42.21/27.16 tptp_fun_B_5: $i)).
% 42.21/27.16 tff(tptp_fun_B_0_type, type, (
% 42.21/27.16 tptp_fun_B_0: $i > $i)).
% 42.21/27.16 tff(empty_set_type, type, (
% 42.21/27.16 empty_set: $i)).
% 42.21/27.16 tff(disjoint_type, type, (
% 42.21/27.16 disjoint: ( $i * $i ) > $o)).
% 42.21/27.16 tff(tptp_fun_C_7_type, type, (
% 42.21/27.16 tptp_fun_C_7: $i)).
% 42.21/27.16 tff(1,plain,
% 42.21/27.16 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 42.21/27.16 inference(bind,[status(th)],[])).
% 42.21/27.16 tff(2,plain,
% 42.21/27.16 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 42.21/27.16 inference(quant_intro,[status(thm)],[1])).
% 42.21/27.16 tff(3,plain,
% 42.21/27.16 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 42.21/27.16 inference(rewrite,[status(thm)],[])).
% 42.21/27.16 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 42.21/27.16 tff(5,plain,
% 42.21/27.16 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 42.21/27.16 inference(modus_ponens,[status(thm)],[4, 3])).
% 42.21/27.16 tff(6,plain,(
% 42.21/27.16 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 42.21/27.16 inference(skolemize,[status(sab)],[5])).
% 42.21/27.16 tff(7,plain,
% 42.21/27.16 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 42.21/27.16 inference(modus_ponens,[status(thm)],[6, 2])).
% 42.21/27.16 tff(8,plain,
% 42.21/27.16 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6))),
% 42.21/27.16 inference(quant_inst,[status(thm)],[])).
% 42.21/27.16 tff(9,plain,
% 42.21/27.16 (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6)),
% 42.21/27.16 inference(unit_resolution,[status(thm)],[8, 7])).
% 42.21/27.16 tff(10,plain,
% 42.21/27.16 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5)) <=> in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))),
% 42.21/27.16 inference(monotonicity,[status(thm)],[9])).
% 42.21/27.16 tff(11,plain,
% 42.21/27.16 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)) <=> in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 42.21/27.16 inference(symmetry,[status(thm)],[10])).
% 42.21/27.16 tff(12,assumption,(in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))), introduced(assumption)).
% 42.21/27.16 tff(13,plain,
% 42.21/27.16 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 42.21/27.16 inference(modus_ponens,[status(thm)],[12, 11])).
% 42.21/27.16 tff(14,plain,
% 42.21/27.16 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 42.21/27.16 inference(bind,[status(th)],[])).
% 42.21/27.16 tff(15,plain,
% 42.21/27.16 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.16 inference(quant_intro,[status(thm)],[14])).
% 42.21/27.16 tff(16,plain,
% 42.21/27.16 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.16 inference(pull_quant,[status(thm)],[])).
% 42.21/27.16 tff(17,plain,
% 42.21/27.16 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(18,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[17])).
% 42.21/27.17 tff(19,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(transitivity,[status(thm)],[18, 16])).
% 42.21/27.17 tff(20,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(transitivity,[status(thm)],[19, 15])).
% 42.21/27.17 tff(21,plain,
% 42.21/27.17 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(22,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[21])).
% 42.21/27.17 tff(23,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(transitivity,[status(thm)],[22, 20])).
% 42.21/27.17 tff(24,plain,
% 42.21/27.17 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(25,plain,
% 42.21/27.17 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[24])).
% 42.21/27.17 tff(26,plain,
% 42.21/27.17 (^[A: $i] : rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(27,plain,
% 42.21/27.17 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[26])).
% 42.21/27.17 tff(28,plain,
% 42.21/27.17 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(29,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 42.21/27.17 tff(30,plain,
% 42.21/27.17 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[29, 28])).
% 42.21/27.17 tff(31,plain,(
% 42.21/27.17 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(skolemize,[status(sab)],[30])).
% 42.21/27.17 tff(32,plain,
% 42.21/27.17 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[31, 27])).
% 42.21/27.17 tff(33,plain,
% 42.21/27.17 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[32, 25])).
% 42.21/27.17 tff(34,plain,
% 42.21/27.17 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[33, 23])).
% 42.21/27.17 tff(35,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(36,plain,
% 42.21/27.17 (~((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5)))))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[35, 34])).
% 42.21/27.17 tff(37,plain,
% 42.21/27.17 (((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5))))) | ((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(38,plain,
% 42.21/27.17 ((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5)))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[37, 36])).
% 42.21/27.17 tff(39,plain,
% 42.21/27.17 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(40,plain,
% 42.21/27.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[39])).
% 42.21/27.17 tff(41,plain,
% 42.21/27.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(42,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 42.21/27.17 tff(43,plain,
% 42.21/27.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[42, 41])).
% 42.21/27.17 tff(44,plain,(
% 42.21/27.17 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 42.21/27.17 inference(skolemize,[status(sab)],[43])).
% 42.21/27.17 tff(45,plain,
% 42.21/27.17 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[44, 40])).
% 42.21/27.17 tff(46,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(47,plain,
% 42.21/27.17 (disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[46, 45])).
% 42.21/27.17 tff(48,assumption,(~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))), introduced(assumption)).
% 42.21/27.17 tff(49,plain,
% 42.21/27.17 (((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))) | disjoint(A!6, B!5)),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(50,plain,
% 42.21/27.17 (disjoint(A!6, B!5)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[49, 48])).
% 42.21/27.17 tff(51,plain,
% 42.21/27.17 ((~(disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))) | (~disjoint(A!6, B!5)) | (set_intersection2(A!6, B!5) = empty_set)),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(52,plain,
% 42.21/27.17 ((~(disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))) | (set_intersection2(A!6, B!5) = empty_set)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[51, 50])).
% 42.21/27.17 tff(53,plain,
% 42.21/27.17 (set_intersection2(A!6, B!5) = empty_set),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[52, 47])).
% 42.21/27.17 tff(54,plain,
% 42.21/27.17 (((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))) | in(C!7, set_intersection2(A!6, B!5))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(55,plain,
% 42.21/27.17 (in(C!7, set_intersection2(A!6, B!5))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[54, 48])).
% 42.21/27.17 tff(56,plain,
% 42.21/27.17 ((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5)))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(57,plain,
% 42.21/27.17 ((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(set_intersection2(A!6, B!5) = empty_set))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[56, 55])).
% 42.21/27.17 tff(58,plain,
% 42.21/27.17 ($false),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[57, 53, 38])).
% 42.21/27.17 tff(59,plain,((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 42.21/27.17 tff(60,plain,
% 42.21/27.17 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(61,plain,
% 42.21/27.17 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) <=> (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(62,plain,
% 42.21/27.17 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(monotonicity,[status(thm)],[61])).
% 42.21/27.17 tff(63,plain,
% 42.21/27.17 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))))),
% 42.21/27.17 inference(transitivity,[status(thm)],[62, 60])).
% 42.21/27.17 tff(64,plain,
% 42.21/27.17 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(65,plain,
% 42.21/27.17 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(66,plain,
% 42.21/27.17 ((in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)) <=> (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(67,plain,
% 42.21/27.17 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) <=> (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(68,plain,
% 42.21/27.17 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(monotonicity,[status(thm)],[67, 66])).
% 42.21/27.17 tff(69,plain,
% 42.21/27.17 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(transitivity,[status(thm)],[68, 65])).
% 42.21/27.17 tff(70,plain,
% 42.21/27.17 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(71,plain,
% 42.21/27.17 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) <=> ((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(72,plain,
% 42.21/27.17 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 42.21/27.17 inference(monotonicity,[status(thm)],[71])).
% 42.21/27.17 tff(73,plain,
% 42.21/27.17 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 42.21/27.17 inference(transitivity,[status(thm)],[72, 70])).
% 42.21/27.17 tff(74,plain,
% 42.21/27.17 ((~![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)))))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(75,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/sandbox/benchmark/theBenchmark.p','t4_xboole_0')).
% 42.21/27.17 tff(76,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[75, 74])).
% 42.21/27.17 tff(77,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[76, 74])).
% 42.21/27.17 tff(78,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[77, 74])).
% 42.21/27.17 tff(79,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[78, 74])).
% 42.21/27.17 tff(80,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[79, 74])).
% 42.21/27.17 tff(81,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[80, 74])).
% 42.21/27.17 tff(82,plain,
% 42.21/27.17 (~![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))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[81, 74])).
% 42.21/27.17 tff(83,plain,
% 42.21/27.17 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[82, 73])).
% 42.21/27.17 tff(84,plain,
% 42.21/27.17 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[83, 69])).
% 42.21/27.17 tff(85,plain,
% 42.21/27.17 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[84, 64])).
% 42.21/27.17 tff(86,plain,
% 42.21/27.17 ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[85, 63])).
% 42.21/27.17 tff(87,plain,
% 42.21/27.17 (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[86, 59])).
% 42.21/27.17 tff(88,plain,
% 42.21/27.17 ((disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))) | ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(89,plain,
% 42.21/27.17 (![C: $i] : (~in(C, set_intersection2(A!6, B!5)))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[88, 87])).
% 42.21/27.17 tff(90,plain,
% 42.21/27.17 ((~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5)))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(91,plain,
% 42.21/27.17 (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[90, 89])).
% 42.21/27.17 tff(92,plain,
% 42.21/27.17 ($false),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[91, 13])).
% 42.21/27.17 tff(93,plain,(~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))), inference(lemma,lemma(discharge,[]))).
% 42.21/27.17 tff(94,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(95,plain,
% 42.21/27.17 (disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[94, 45])).
% 42.21/27.17 tff(96,plain,
% 42.21/27.17 ((disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))) | (~disjoint(A!6, B!5))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(97,plain,
% 42.21/27.17 (~disjoint(A!6, B!5)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[96, 87])).
% 42.21/27.17 tff(98,plain,
% 42.21/27.17 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(99,plain,
% 42.21/27.17 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[98])).
% 42.21/27.17 tff(100,plain,
% 42.21/27.17 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(101,plain,
% 42.21/27.17 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 42.21/27.17 inference(bind,[status(th)],[])).
% 42.21/27.17 tff(102,plain,
% 42.21/27.17 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(quant_intro,[status(thm)],[101])).
% 42.21/27.17 tff(103,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 42.21/27.17 tff(104,plain,
% 42.21/27.17 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[103, 102])).
% 42.21/27.17 tff(105,plain,
% 42.21/27.17 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[104, 100])).
% 42.21/27.17 tff(106,plain,(
% 42.21/27.17 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(skolemize,[status(sab)],[105])).
% 42.21/27.17 tff(107,plain,
% 42.21/27.17 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[106, 99])).
% 42.21/27.17 tff(108,plain,
% 42.21/27.17 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!5, A!6)) | disjoint(A!6, B!5))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!5, A!6)) | disjoint(A!6, B!5))),
% 42.21/27.17 inference(rewrite,[status(thm)],[])).
% 42.21/27.17 tff(109,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!5, A!6)) | disjoint(A!6, B!5))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(110,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!5, A!6)) | disjoint(A!6, B!5)),
% 42.21/27.17 inference(modus_ponens,[status(thm)],[109, 108])).
% 42.21/27.17 tff(111,plain,
% 42.21/27.17 (~disjoint(B!5, A!6)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[110, 107, 97])).
% 42.21/27.17 tff(112,plain,
% 42.21/27.17 ((~(disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))) | disjoint(B!5, A!6) | (~(set_intersection2(B!5, A!6) = empty_set))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(113,plain,
% 42.21/27.17 ((~(disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))) | (~(set_intersection2(B!5, A!6) = empty_set))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[112, 111])).
% 42.21/27.17 tff(114,plain,
% 42.21/27.17 (~(set_intersection2(B!5, A!6) = empty_set)),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[113, 95])).
% 42.21/27.17 tff(115,plain,
% 42.21/27.17 ((~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))) | (set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(116,plain,
% 42.21/27.17 (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[115, 114, 93])).
% 42.21/27.17 tff(117,plain,
% 42.21/27.17 (((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | ((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))),
% 42.21/27.17 inference(tautology,[status(thm)],[])).
% 42.21/27.17 tff(118,plain,
% 42.21/27.17 ((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[117, 116])).
% 42.21/27.17 tff(119,plain,
% 42.21/27.17 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))))),
% 42.21/27.17 inference(quant_inst,[status(thm)],[])).
% 42.21/27.17 tff(120,plain,
% 42.21/27.17 ($false),
% 42.21/27.17 inference(unit_resolution,[status(thm)],[119, 34, 118])).
% 42.21/27.17 % SZS output end Proof
%------------------------------------------------------------------------------