TSTP Solution File: SET907+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:08:34 EDT 2022
% Result : Theorem 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n018.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Sep 3 08:34:59 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.36 % SZS status Theorem
% 0.17/0.36 % SZS output start Proof
% 0.17/0.36 tff(in_type, type, (
% 0.17/0.36 in: ( $i * $i ) > $o)).
% 0.17/0.36 tff(tptp_fun_B_3_type, type, (
% 0.17/0.36 tptp_fun_B_3: $i)).
% 0.17/0.36 tff(tptp_fun_C_2_type, type, (
% 0.17/0.36 tptp_fun_C_2: $i)).
% 0.17/0.36 tff(tptp_fun_A_4_type, type, (
% 0.17/0.36 tptp_fun_A_4: $i)).
% 0.17/0.36 tff(subset_type, type, (
% 0.17/0.36 subset: ( $i * $i ) > $o)).
% 0.17/0.36 tff(unordered_pair_type, type, (
% 0.17/0.36 unordered_pair: ( $i * $i ) > $i)).
% 0.17/0.36 tff(set_union2_type, type, (
% 0.17/0.36 set_union2: ( $i * $i ) > $i)).
% 0.17/0.36 tff(1,plain,
% 0.17/0.36 ((~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(2,plain,
% 0.17/0.36 ((~![A: $i, B: $i, C: $i] : ((in(A, B) & in(C, B)) => (set_union2(unordered_pair(A, C), B) = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(3,axiom,(~![A: $i, B: $i, C: $i] : ((in(A, B) & in(C, B)) => (set_union2(unordered_pair(A, C), B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_zfmisc_1')).
% 0.17/0.36 tff(4,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.17/0.36 tff(5,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.17/0.36 tff(6,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.17/0.36 tff(7,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.17/0.36 tff(8,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.17/0.36 tff(9,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.17/0.36 tff(10,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i] : ((~(in(A, B) & in(C, B))) | (set_union2(unordered_pair(A, C), B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.17/0.36 tff(11,plain,(
% 0.17/0.36 ~((~(in(A!4, B!3) & in(C!2, B!3))) | (set_union2(unordered_pair(A!4, C!2), B!3) = B!3))),
% 0.17/0.36 inference(skolemize,[status(sab)],[10])).
% 0.17/0.36 tff(12,plain,
% 0.17/0.36 (in(A!4, B!3) & in(C!2, B!3)),
% 0.17/0.36 inference(or_elim,[status(thm)],[11])).
% 0.17/0.36 tff(13,plain,
% 0.17/0.36 (in(C!2, B!3)),
% 0.17/0.36 inference(and_elim,[status(thm)],[12])).
% 0.17/0.36 tff(14,plain,
% 0.17/0.36 (in(A!4, B!3)),
% 0.17/0.36 inference(and_elim,[status(thm)],[12])).
% 0.17/0.36 tff(15,plain,
% 0.17/0.36 ((~((~in(A!4, B!3)) | (~in(C!2, B!3)))) | (~in(A!4, B!3)) | (~in(C!2, B!3))),
% 0.17/0.36 inference(tautology,[status(thm)],[])).
% 0.17/0.36 tff(16,plain,
% 0.17/0.36 (~((~in(A!4, B!3)) | (~in(C!2, B!3)))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.17/0.36 tff(17,plain,
% 0.17/0.36 (~(set_union2(unordered_pair(A!4, C!2), B!3) = B!3)),
% 0.17/0.36 inference(or_elim,[status(thm)],[11])).
% 0.17/0.36 tff(18,plain,
% 0.17/0.36 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(19,plain,
% 0.17/0.36 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[18])).
% 0.17/0.36 tff(20,plain,
% 0.17/0.36 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(21,plain,
% 0.17/0.36 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(22,plain,
% 0.17/0.36 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[21])).
% 0.17/0.36 tff(23,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.17/0.36 tff(24,plain,
% 0.17/0.36 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.17/0.36 tff(25,plain,
% 0.17/0.36 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.17/0.36 tff(26,plain,(
% 0.17/0.36 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(skolemize,[status(sab)],[25])).
% 0.17/0.36 tff(27,plain,
% 0.17/0.36 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.17/0.36 tff(28,plain,
% 0.17/0.36 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(unordered_pair(A!4, C!2), B!3)) | (set_union2(unordered_pair(A!4, C!2), B!3) = B!3))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(unordered_pair(A!4, C!2), B!3)) | (set_union2(unordered_pair(A!4, C!2), B!3) = B!3))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(29,plain,
% 0.17/0.36 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(unordered_pair(A!4, C!2), B!3)) | (set_union2(unordered_pair(A!4, C!2), B!3) = B!3))),
% 0.17/0.36 inference(quant_inst,[status(thm)],[])).
% 0.17/0.36 tff(30,plain,
% 0.17/0.36 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(unordered_pair(A!4, C!2), B!3)) | (set_union2(unordered_pair(A!4, C!2), B!3) = B!3)),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.17/0.36 tff(31,plain,
% 0.17/0.36 (~subset(unordered_pair(A!4, C!2), B!3)),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.17/0.36 tff(32,plain,
% 0.17/0.36 ((~(subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3)))))) | subset(unordered_pair(A!4, C!2), B!3) | ((~in(A!4, B!3)) | (~in(C!2, B!3)))),
% 0.17/0.36 inference(tautology,[status(thm)],[])).
% 0.17/0.36 tff(33,plain,
% 0.17/0.36 (~(subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3)))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[32, 31, 16])).
% 0.17/0.36 tff(34,plain,
% 0.17/0.36 (^[A: $i, B: $i, C: $i] : refl((subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))) <=> (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(35,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))) <=> ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.17/0.36 tff(36,plain,
% 0.17/0.36 (^[A: $i, B: $i, C: $i] : rewrite((subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(37,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[36])).
% 0.17/0.36 tff(38,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(39,axiom,(![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 0.17/0.36 tff(40,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.17/0.36 tff(41,plain,(
% 0.17/0.36 ![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 0.17/0.36 inference(skolemize,[status(sab)],[40])).
% 0.17/0.36 tff(42,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.17/0.36 tff(43,plain,
% 0.17/0.36 (![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.17/0.36 tff(44,plain,
% 0.17/0.36 (((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(45,plain,
% 0.17/0.37 ((subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(C!2, B!3)) | (~in(A!4, B!3))))) <=> (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3)))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(46,plain,
% 0.17/0.37 (((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(C!2, B!3)) | (~in(A!4, B!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3))))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[45])).
% 0.17/0.37 tff(47,plain,
% 0.17/0.37 (((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(C!2, B!3)) | (~in(A!4, B!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[46, 44])).
% 0.17/0.37 tff(48,plain,
% 0.17/0.37 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(C!2, B!3)) | (~in(A!4, B!3)))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(49,plain,
% 0.17/0.37 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (~((~in(B, C)) | (~in(A, C)))))) | (subset(unordered_pair(A!4, C!2), B!3) <=> (~((~in(A!4, B!3)) | (~in(C!2, B!3)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.17/0.37 tff(50,plain,
% 0.17/0.37 ($false),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 0.17/0.37 % SZS output end Proof
%------------------------------------------------------------------------------