TSTP Solution File: SEU150+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU150+1 : 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 07:27:47 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Sep 3 10:03:18 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 tff(unordered_pair_type, type, (
% 0.14/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.14/0.38 tff(tptp_fun_B_1_type, type, (
% 0.14/0.38 tptp_fun_B_1: $i)).
% 0.14/0.38 tff(tptp_fun_C_0_type, type, (
% 0.14/0.38 tptp_fun_C_0: $i)).
% 0.14/0.38 tff(singleton_type, type, (
% 0.14/0.38 singleton: $i > $i)).
% 0.14/0.38 tff(tptp_fun_A_2_type, type, (
% 0.14/0.38 tptp_fun_A_2: $i)).
% 0.14/0.38 tff(1,plain,
% 0.14/0.38 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(2,plain,
% 0.14/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.38 tff(3,plain,
% 0.14/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(4,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.14/0.38 tff(5,plain,
% 0.14/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.38 tff(6,plain,(
% 0.14/0.38 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.38 inference(skolemize,[status(sab)],[5])).
% 0.14/0.38 tff(7,plain,
% 0.14/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.38 tff(8,plain,
% 0.14/0.38 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!1, C!0) = unordered_pair(C!0, B!1))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(9,plain,
% 0.14/0.38 (unordered_pair(B!1, C!0) = unordered_pair(C!0, B!1)),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.38 tff(10,plain,
% 0.14/0.38 ((~![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)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(11,plain,
% 0.14/0.38 ((~![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)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(12,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t9_zfmisc_1')).
% 0.14/0.38 tff(13,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.38 tff(14,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.14/0.38 tff(15,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.38 tff(16,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.14/0.38 tff(17,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.14/0.38 tff(18,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.14/0.38 tff(19,plain,
% 0.14/0.38 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (B = C))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.14/0.38 tff(20,plain,(
% 0.14/0.38 ~((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (B!1 = C!0))),
% 0.14/0.38 inference(skolemize,[status(sab)],[19])).
% 0.14/0.38 tff(21,plain,
% 0.14/0.38 (singleton(A!2) = unordered_pair(B!1, C!0)),
% 0.14/0.38 inference(or_elim,[status(thm)],[20])).
% 0.14/0.38 tff(22,plain,
% 0.14/0.38 (^[A: $i, B: $i, C: $i] : refl(((~(singleton(A) = unordered_pair(B, C))) | (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(23,plain,
% 0.14/0.38 (![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))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (![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))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 (^[A: $i, B: $i, C: $i] : rewrite(((singleton(A) = unordered_pair(B, C)) => (A = B)) <=> ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (![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))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.39 tff(27,axiom,(![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.14/0.39 tff(30,plain,(
% 0.14/0.39 ![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.14/0.39 inference(skolemize,[status(sab)],[29])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(A!2) = unordered_pair(B!1, C!0))) | (A!2 = B!1)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (A!2 = B!1),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 (B!1 = A!2),
% 0.14/0.39 inference(symmetry,[status(thm)],[35])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (singleton(B!1) = singleton(A!2)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 (singleton(B!1) = unordered_pair(C!0, B!1)),
% 0.14/0.39 inference(transitivity,[status(thm)],[37, 21, 9])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (~(B!1 = C!0)),
% 0.14/0.39 inference(or_elim,[status(thm)],[20])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))) <=> ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | ((~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) | (~(singleton(B!1) = unordered_pair(C!0, B!1))) | (B!1 = C!0)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 (~(singleton(B!1) = unordered_pair(C!0, B!1))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[42, 31, 39])).
% 0.14/0.39 tff(44,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------