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
%------------------------------------------------------------------------------