TSTP Solution File: SYN002-1.007.008 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN002-1.007.008 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Thu Sep 29 23:53:07 EDT 2022
% Result : Unsatisfiable 1.20s 1.02s
% Output : Proof 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN002-1.007.008 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 : Mon Sep 5 01:03:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.20/1.02 % SZS status Unsatisfiable
% 1.20/1.02 % SZS output start Proof
% 1.20/1.02 tff(p_type, type, (
% 1.20/1.02 p: $i > $o)).
% 1.20/1.02 tff(f_type, type, (
% 1.20/1.02 f: $i > $i)).
% 1.20/1.02 tff(elem_0_type, type, (
% 1.20/1.02 elem_0: $i)).
% 1.20/1.02 tff(1,assumption,(~p(f(f(f(f(f(f(f(f(elem!0)))))))))), introduced(assumption)).
% 1.20/1.02 tff(2,assumption,(~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))), introduced(assumption)).
% 1.20/1.02 tff(3,plain,
% 1.20/1.02 (^[X: $i] : refl((p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> (p(X) | p(f(f(f(f(f(f(f(X))))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(4,plain,
% 1.20/1.02 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[3])).
% 1.20/1.02 tff(5,plain,
% 1.20/1.02 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(6,axiom,(![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','positive')).
% 1.20/1.02 tff(7,plain,
% 1.20/1.02 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.20/1.02 tff(8,plain,(
% 1.20/1.02 ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 1.20/1.02 inference(skolemize,[status(sab)],[7])).
% 1.20/1.02 tff(9,plain,
% 1.20/1.02 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.20/1.02 tff(10,plain,
% 1.20/1.02 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(11,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(12,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.20/1.02 tff(13,plain,
% 1.20/1.02 ($false),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[12, 9, 1, 2])).
% 1.20/1.02 tff(14,plain,(p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(elem!0)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.02 tff(15,plain,
% 1.20/1.02 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[14, 1])).
% 1.20/1.02 tff(16,plain,
% 1.20/1.02 (^[X: $i] : refl(((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(17,plain,
% 1.20/1.02 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[16])).
% 1.20/1.02 tff(18,plain,
% 1.20/1.02 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(19,axiom,(![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','negative')).
% 1.20/1.02 tff(20,plain,
% 1.20/1.02 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.20/1.02 tff(21,plain,(
% 1.20/1.02 ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 1.20/1.02 inference(skolemize,[status(sab)],[20])).
% 1.20/1.02 tff(22,plain,
% 1.20/1.02 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.20/1.02 tff(23,plain,
% 1.20/1.02 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(24,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(25,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.20/1.02 tff(26,plain,
% 1.20/1.02 ((~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[25, 22])).
% 1.20/1.02 tff(27,plain,
% 1.20/1.02 (~p(f(f(f(f(f(f(f(elem!0))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[26, 15])).
% 1.20/1.02 tff(28,plain,
% 1.20/1.02 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(29,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(30,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.20/1.02 tff(31,plain,
% 1.20/1.02 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[30, 9, 27])).
% 1.20/1.02 tff(32,plain,
% 1.20/1.02 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(33,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(34,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.20/1.02 tff(35,plain,
% 1.20/1.02 (~p(f(f(f(f(f(f(elem!0)))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[34, 22, 31])).
% 1.20/1.02 tff(36,plain,
% 1.20/1.02 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(37,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(38,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.20/1.02 tff(39,plain,
% 1.20/1.02 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[38, 9, 35])).
% 1.20/1.02 tff(40,plain,
% 1.20/1.02 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(41,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(42,plain,
% 1.20/1.02 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.20/1.02 tff(43,plain,
% 1.20/1.02 (~p(f(f(f(f(f(elem!0))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[42, 22, 39])).
% 1.20/1.02 tff(44,plain,
% 1.20/1.02 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(45,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(46,plain,
% 1.20/1.02 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.20/1.02 tff(47,plain,
% 1.20/1.02 (p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[46, 9, 43])).
% 1.20/1.02 tff(48,plain,
% 1.20/1.02 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.03 inference(rewrite,[status(thm)],[])).
% 1.20/1.03 tff(49,plain,
% 1.20/1.03 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 1.20/1.03 inference(quant_inst,[status(thm)],[])).
% 1.20/1.03 tff(50,plain,
% 1.20/1.03 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 1.20/1.03 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.20/1.03 tff(51,plain,
% 1.20/1.03 (~p(f(f(f(f(elem!0)))))),
% 1.20/1.03 inference(unit_resolution,[status(thm)],[50, 22, 47])).
% 1.20/1.03 tff(52,plain,
% 1.20/1.03 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 1.20/1.03 inference(rewrite,[status(thm)],[])).
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% 1.20/1.03 inference(quant_inst,[status(thm)],[])).
% 1.20/1.03 tff(157,plain,
% 1.20/1.03 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 1.20/1.03 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.20/1.03 tff(158,plain,
% 1.20/1.03 (p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 1.20/1.03 inference(unit_resolution,[status(thm)],[157, 9])).
% 1.20/1.03 tff(159,plain,
% 1.20/1.03 ($false),
% 1.20/1.03 inference(unit_resolution,[status(thm)],[158, 154, 137])).
% 1.20/1.03 % SZS output end Proof
%------------------------------------------------------------------------------