TSTP Solution File: SEU141+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 07:27:43 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 09:59:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(empty_set_type, type, (
% 0.18/0.48 empty_set: $i)).
% 0.18/0.48 tff(set_intersection2_type, type, (
% 0.18/0.48 set_intersection2: ( $i * $i ) > $i)).
% 0.18/0.48 tff(tptp_fun_B_10_type, type, (
% 0.18/0.48 tptp_fun_B_10: $i)).
% 0.18/0.48 tff(tptp_fun_A_11_type, type, (
% 0.18/0.48 tptp_fun_A_11: $i)).
% 0.18/0.48 tff(set_difference_type, type, (
% 0.18/0.48 set_difference: ( $i * $i ) > $i)).
% 0.18/0.48 tff(subset_type, type, (
% 0.18/0.48 subset: ( $i * $i ) > $o)).
% 0.18/0.48 tff(set_union2_type, type, (
% 0.18/0.48 set_union2: ( $i * $i ) > $i)).
% 0.18/0.48 tff(disjoint_type, type, (
% 0.18/0.48 disjoint: ( $i * $i ) > $o)).
% 0.18/0.48 tff(in_type, type, (
% 0.18/0.48 in: ( $i * $i ) > $o)).
% 0.18/0.48 tff(tptp_fun_C_2_type, type, (
% 0.18/0.48 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.18/0.48 tff(1,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl(((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ((set_difference(A, B) = empty_set) <=> subset(A, B)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B)) <=> ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(4,axiom,(![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l32_xboole_1')).
% 0.18/0.48 tff(5,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.48 tff(6,plain,(
% 0.18/0.48 ![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.18/0.48 inference(skolemize,[status(sab)],[5])).
% 0.18/0.48 tff(7,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.48 tff(8,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(9,plain,
% 0.18/0.48 ((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.48 tff(10,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(11,plain,
% 0.18/0.48 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.48 tff(12,plain,
% 0.18/0.48 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(13,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 0.18/0.48 tff(14,plain,
% 0.18/0.48 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.48 tff(15,plain,(
% 0.18/0.48 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.18/0.48 inference(skolemize,[status(sab)],[14])).
% 0.18/0.48 tff(16,plain,
% 0.18/0.48 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.48 tff(17,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(A!11, B!10), A!11)),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(18,plain,
% 0.18/0.48 (subset(set_difference(A!11, B!10), A!11)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.48 tff(19,plain,
% 0.18/0.48 ((~((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))) | (set_difference(set_difference(A!11, B!10), A!11) = empty_set) | (~subset(set_difference(A!11, B!10), A!11))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(20,plain,
% 0.18/0.48 ((~((set_difference(set_difference(A!11, B!10), A!11) = empty_set) <=> subset(set_difference(A!11, B!10), A!11))) | (set_difference(set_difference(A!11, B!10), A!11) = empty_set)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.48 tff(21,plain,
% 0.18/0.48 (set_difference(set_difference(A!11, B!10), A!11) = empty_set),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.18/0.48 tff(22,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(23,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.48 tff(24,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(25,plain,
% 0.18/0.48 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(26,plain,
% 0.18/0.48 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.48 tff(27,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.18/0.48 tff(28,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.48 tff(29,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.48 tff(30,plain,(
% 0.18/0.48 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[29])).
% 0.18/0.48 tff(31,plain,
% 0.18/0.48 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.48 tff(32,plain,
% 0.18/0.48 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(33,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(34,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), A!11)) | (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.48 tff(35,plain,
% 0.18/0.48 (A!11 = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[34, 31, 18])).
% 0.18/0.48 tff(36,plain,
% 0.18/0.48 (set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))) = A!11),
% 0.18/0.48 inference(symmetry,[status(thm)],[35])).
% 0.18/0.48 tff(37,plain,
% 0.18/0.48 (set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), A!11)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.48 tff(38,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl((set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(39,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.48 tff(40,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)) <=> ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(41,axiom,(![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_xboole_1')).
% 0.18/0.48 tff(42,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.48 tff(43,plain,(
% 0.18/0.48 ![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.18/0.48 inference(skolemize,[status(sab)],[42])).
% 0.18/0.48 tff(44,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.18/0.48 tff(45,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) | (set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(46,plain,
% 0.18/0.48 (set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_difference(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.18/0.48 tff(47,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl((set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(48,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.48 tff(49,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)) <=> ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(50,axiom,(![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_xboole_1')).
% 0.18/0.48 tff(51,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.48 tff(52,plain,(
% 0.18/0.48 ![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.18/0.48 inference(skolemize,[status(sab)],[51])).
% 0.18/0.48 tff(53,plain,
% 0.18/0.48 (![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.48 tff(54,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : (set_difference(A, set_difference(A, B)) = set_intersection2(A, B))) | (set_difference(A!11, set_difference(A!11, B!10)) = set_intersection2(A!11, B!10))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(55,plain,
% 0.18/0.48 (set_difference(A!11, set_difference(A!11, B!10)) = set_intersection2(A!11, B!10)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.18/0.48 tff(56,plain,
% 0.18/0.48 (set_intersection2(A!11, B!10) = set_difference(A!11, set_difference(A!11, B!10))),
% 0.18/0.48 inference(symmetry,[status(thm)],[55])).
% 0.18/0.48 tff(57,assumption,(~(set_difference(A!11, B!10) = A!11)), introduced(assumption)).
% 0.18/0.48 tff(58,plain,
% 0.18/0.48 ((~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11))) <=> ((~disjoint(A!11, B!10)) <=> (set_difference(A!11, B!10) = A!11))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(59,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) <=> (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(60,axiom,(~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t83_xboole_1')).
% 0.18/0.48 tff(61,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.18/0.48 tff(63,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.18/0.48 tff(64,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[64, 59])).
% 0.18/0.48 tff(66,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.18/0.48 tff(67,plain,
% 0.18/0.48 (~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.48 tff(68,plain,(
% 0.18/0.48 ~(disjoint(A!11, B!10) <=> (set_difference(A!11, B!10) = A!11))),
% 0.18/0.48 inference(skolemize,[status(sab)],[67])).
% 0.18/0.48 tff(69,plain,
% 0.18/0.48 ((~disjoint(A!11, B!10)) <=> (set_difference(A!11, B!10) = A!11)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.18/0.48 tff(70,plain,
% 0.18/0.48 (disjoint(A!11, B!10) | (set_difference(A!11, B!10) = A!11) | (~((~disjoint(A!11, B!10)) <=> (set_difference(A!11, B!10) = A!11)))),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(71,plain,
% 0.18/0.48 (disjoint(A!11, B!10) | (set_difference(A!11, B!10) = A!11)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.18/0.48 tff(72,plain,
% 0.18/0.48 (disjoint(A!11, B!10)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[71, 57])).
% 0.18/0.48 tff(73,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(74,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.48 tff(75,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(76,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.18/0.48 tff(77,plain,
% 0.18/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.48 tff(78,plain,(
% 0.18/0.48 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.18/0.48 inference(skolemize,[status(sab)],[77])).
% 0.18/0.48 tff(79,plain,
% 0.18/0.48 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.48 tff(80,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(81,plain,
% 0.18/0.48 (disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.48 tff(82,plain,
% 0.18/0.48 ((~(disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))) | (~disjoint(A!11, B!10)) | (set_intersection2(A!11, B!10) = empty_set)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(83,plain,
% 0.18/0.48 ((~disjoint(A!11, B!10)) | (set_intersection2(A!11, B!10) = empty_set)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.18/0.48 tff(84,plain,
% 0.18/0.48 (set_intersection2(A!11, B!10) = empty_set),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[83, 72])).
% 0.18/0.48 tff(85,plain,
% 0.18/0.48 (empty_set = set_intersection2(A!11, B!10)),
% 0.18/0.48 inference(symmetry,[status(thm)],[84])).
% 0.18/0.48 tff(86,plain,
% 0.18/0.48 ((~![A: $i, B: $i] : ((set_difference(A, B) = empty_set) <=> subset(A, B))) | ((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(87,plain,
% 0.18/0.48 ((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[86, 7])).
% 0.18/0.48 tff(88,plain,
% 0.18/0.48 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(89,plain,
% 0.18/0.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.48 tff(90,plain,
% 0.18/0.48 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(91,plain,
% 0.18/0.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.48 tff(92,plain,
% 0.18/0.48 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.48 tff(93,plain,
% 0.18/0.48 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.49 tff(95,plain,
% 0.18/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(96,plain,
% 0.18/0.49 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(97,plain,
% 0.18/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.49 tff(98,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.18/0.49 tff(99,plain,
% 0.18/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.49 tff(100,plain,
% 0.18/0.49 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.18/0.49 tff(101,plain,(
% 0.18/0.49 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.18/0.49 inference(skolemize,[status(sab)],[100])).
% 0.18/0.49 tff(102,plain,
% 0.18/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.18/0.49 tff(103,plain,
% 0.18/0.49 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.18/0.49 tff(104,plain,
% 0.18/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(105,plain,
% 0.18/0.49 ((~(~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(106,plain,
% 0.18/0.49 (($false | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))) <=> (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(107,plain,
% 0.18/0.49 ((~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10)))))) <=> (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(108,plain,
% 0.18/0.49 ((~$true) <=> $false),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(109,plain,
% 0.18/0.49 (((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | $true) <=> $true),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(110,plain,
% 0.18/0.49 (![C: $i] : $true <=> $true),
% 0.18/0.49 inference(elim_unused_vars,[status(thm)],[])).
% 0.18/0.49 tff(111,plain,
% 0.18/0.49 (![C: $i] : $true <=> ![C: $i] : $true),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(112,plain,
% 0.18/0.49 (![C: $i] : $true <=> $true),
% 0.18/0.49 inference(transitivity,[status(thm)],[111, 110])).
% 0.18/0.49 tff(113,plain,
% 0.18/0.49 (^[C: $i] : rewrite(((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))) <=> $true)),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(114,plain,
% 0.18/0.49 (![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))) <=> ![C: $i] : $true),
% 0.18/0.49 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.49 tff(115,plain,
% 0.18/0.49 (![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))) <=> $true),
% 0.18/0.49 inference(transitivity,[status(thm)],[114, 112])).
% 0.18/0.49 tff(116,plain,
% 0.18/0.49 (((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10)))) <=> ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | $true)),
% 0.18/0.49 inference(monotonicity,[status(thm)],[115])).
% 0.18/0.49 tff(117,plain,
% 0.18/0.49 (((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10)))) <=> $true),
% 0.18/0.49 inference(transitivity,[status(thm)],[116, 109])).
% 0.18/0.49 tff(118,plain,
% 0.18/0.49 ((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) <=> (~$true)),
% 0.18/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.49 tff(119,plain,
% 0.18/0.49 ((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) <=> $false),
% 0.18/0.49 inference(transitivity,[status(thm)],[118, 108])).
% 0.18/0.49 tff(120,plain,
% 0.18/0.49 (((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))))))) <=> ($false | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[119, 107])).
% 0.18/0.49 tff(121,plain,
% 0.18/0.49 (((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))))))) <=> (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[120, 106])).
% 0.18/0.49 tff(122,plain,
% 0.18/0.49 ((~((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10)))))))) <=> (~(~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[121])).
% 0.18/0.49 tff(123,plain,
% 0.18/0.49 ((~((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10)))))))) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.18/0.49 inference(transitivity,[status(thm)],[122, 105])).
% 0.18/0.49 tff(124,plain,
% 0.18/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[123])).
% 0.18/0.49 tff(125,plain,
% 0.18/0.49 (((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))))))))) <=> ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[124, 104])).
% 0.18/0.49 tff(126,plain,
% 0.18/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | ![C: $i] : ((~in(C, set_difference(A!11, B!10))) | in(C, set_difference(A!11, B!10))))) | (~(subset(set_difference(A!11, B!10), set_difference(A!11, B!10)) | (~((~in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))) | in(tptp_fun_C_2(set_difference(A!11, B!10), set_difference(A!11, B!10)), set_difference(A!11, B!10))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(127,plain,
% 0.18/0.49 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.18/0.49 tff(128,plain,
% 0.18/0.49 (subset(set_difference(A!11, B!10), set_difference(A!11, B!10))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[127, 103])).
% 0.18/0.49 tff(129,plain,
% 0.18/0.49 ((~((set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) <=> subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))) | (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(130,plain,
% 0.18/0.49 (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = empty_set),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[129, 128, 87])).
% 0.18/0.49 tff(131,plain,
% 0.18/0.49 (set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)) = set_difference(A!11, set_difference(A!11, B!10))),
% 0.18/0.49 inference(transitivity,[status(thm)],[130, 85, 56])).
% 0.18/0.49 tff(132,plain,
% 0.18/0.49 (set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10))) = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.49 tff(133,plain,
% 0.18/0.49 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(134,plain,
% 0.18/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(135,plain,
% 0.18/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.18/0.50 tff(136,plain,
% 0.18/0.50 ((~subset(set_difference(A!11, B!10), set_difference(A!11, B!10))) | (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[135, 31])).
% 0.18/0.50 tff(137,plain,
% 0.18/0.50 (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(set_difference(A!11, B!10), set_difference(A!11, B!10)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[136, 128])).
% 0.18/0.50 tff(138,plain,
% 0.18/0.50 (set_difference(A!11, B!10) = A!11),
% 0.18/0.50 inference(transitivity,[status(thm)],[137, 132, 36])).
% 0.18/0.50 tff(139,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[57, 138])).
% 0.18/0.50 tff(140,plain,(set_difference(A!11, B!10) = A!11), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(141,plain,
% 0.18/0.50 (set_difference(A!11, B!10) = set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))),
% 0.18/0.50 inference(transitivity,[status(thm)],[140, 35])).
% 0.18/0.50 tff(142,plain,
% 0.18/0.50 (set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))) = set_union2(set_difference(A!11, B!10), A!11)),
% 0.18/0.50 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.50 tff(143,plain,
% 0.18/0.50 (set_union2(set_difference(A!11, B!10), A!11) = set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.18/0.50 inference(symmetry,[status(thm)],[142])).
% 0.18/0.50 tff(144,plain,
% 0.18/0.50 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(145,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[144])).
% 0.18/0.50 tff(146,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(147,plain,
% 0.18/0.50 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(148,plain,
% 0.18/0.50 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[147])).
% 0.18/0.50 tff(149,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.18/0.50 tff(150,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.50 tff(151,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.18/0.50 tff(152,plain,(
% 0.18/0.50 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(skolemize,[status(sab)],[151])).
% 0.18/0.50 tff(153,plain,
% 0.18/0.50 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.18/0.50 tff(154,plain,
% 0.18/0.50 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(155,plain,
% 0.18/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(156,plain,
% 0.18/0.50 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!11, B!10), A!11)) | (set_union2(set_difference(A!11, B!10), A!11) = A!11)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.50 tff(157,plain,
% 0.18/0.50 (set_union2(set_difference(A!11, B!10), A!11) = A!11),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[156, 153, 18])).
% 0.18/0.50 tff(158,plain,
% 0.18/0.50 (A!11 = set_union2(set_difference(A!11, B!10), A!11)),
% 0.18/0.50 inference(symmetry,[status(thm)],[157])).
% 0.18/0.50 tff(159,plain,
% 0.18/0.50 (A!11 = set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[158, 143])).
% 0.18/0.50 tff(160,plain,
% 0.18/0.50 (set_difference(A!11, set_difference(A!11, B!10)) = set_difference(set_union2(set_difference(A!11, B!10), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10)))), set_union2(set_difference(A!11, B!10), set_difference(A!11, set_difference(A!11, B!10))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[159, 141])).
% 0.18/0.50 tff(161,plain,
% 0.18/0.50 (set_intersection2(A!11, B!10) = empty_set),
% 0.18/0.50 inference(transitivity,[status(thm)],[56, 160, 46, 37, 21])).
% 0.18/0.50 tff(162,plain,
% 0.18/0.50 ((~disjoint(A!11, B!10)) | (~(set_difference(A!11, B!10) = A!11)) | (~((~disjoint(A!11, B!10)) <=> (set_difference(A!11, B!10) = A!11)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(163,plain,
% 0.18/0.50 ((~disjoint(A!11, B!10)) | (~(set_difference(A!11, B!10) = A!11))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[162, 69])).
% 0.18/0.50 tff(164,plain,
% 0.18/0.50 (~disjoint(A!11, B!10)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[163, 140])).
% 0.18/0.50 tff(165,plain,
% 0.18/0.50 ((~(disjoint(A!11, B!10) <=> (set_intersection2(A!11, B!10) = empty_set))) | disjoint(A!11, B!10) | (~(set_intersection2(A!11, B!10) = empty_set))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(166,plain,
% 0.18/0.50 (disjoint(A!11, B!10) | (~(set_intersection2(A!11, B!10) = empty_set))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[165, 81])).
% 0.18/0.50 tff(167,plain,
% 0.18/0.50 (~(set_intersection2(A!11, B!10) = empty_set)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[166, 164])).
% 0.18/0.50 tff(168,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.18/0.50 % SZS output end Proof
%------------------------------------------------------------------------------