TSTP Solution File: SEU150+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 07:27:47 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 10:05:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(unordered_pair_type, type, (
% 0.20/0.41 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_B_14_type, type, (
% 0.20/0.41 tptp_fun_B_14: $i)).
% 0.20/0.41 tff(tptp_fun_C_13_type, type, (
% 0.20/0.41 tptp_fun_C_13: $i)).
% 0.20/0.41 tff(singleton_type, type, (
% 0.20/0.41 singleton: $i > $i)).
% 0.20/0.41 tff(tptp_fun_A_15_type, type, (
% 0.20/0.41 tptp_fun_A_15: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!14, C!13) = unordered_pair(C!13, B!14))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (unordered_pair(B!14, C!13) = unordered_pair(C!13, B!14)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(12,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_zfmisc_1')).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.41 tff(20,plain,(
% 0.20/0.41 ~((~(singleton(A!15) = unordered_pair(B!14, C!13))) | (B!14 = C!13))),
% 0.20/0.41 inference(skolemize,[status(sab)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (singleton(A!15) = unordered_pair(B!14, C!13)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : refl(((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.42 tff(27,axiom,(![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.42 tff(30,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(skolemize,[status(sab)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!15) = unordered_pair(B!14, C!13))) | (A!15 = B!14))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!15) = unordered_pair(B!14, C!13))) | (A!15 = B!14))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!15) = unordered_pair(B!14, C!13))) | (A!15 = B!14))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!15) = unordered_pair(B!14, C!13))) | (A!15 = B!14)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (A!15 = B!14),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (B!14 = A!15),
% 0.20/0.42 inference(symmetry,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (singleton(B!14) = singleton(A!15)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (singleton(B!14) = unordered_pair(C!13, B!14)),
% 0.20/0.42 inference(transitivity,[status(thm)],[37, 21, 9])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (~(B!14 = C!13)),
% 0.20/0.42 inference(or_elim,[status(thm)],[20])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!14) = unordered_pair(C!13, B!14))) | (B!14 = C!13))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!14) = unordered_pair(C!13, B!14))) | (B!14 = C!13))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!14) = unordered_pair(C!13, B!14))) | (B!14 = C!13))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!14) = unordered_pair(C!13, B!14))) | (B!14 = C!13)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (~(singleton(B!14) = unordered_pair(C!13, B!14))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 31, 39])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------