TSTP Solution File: SET018-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : 600s
% DateTime : Tue Jul 19 05:22:37 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 08:18:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 204 clauses, backtracked 36 clauses, performed 2 splits and kept 164 clauses.
% 0.20/0.44 SPASS allocated 63291 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.02 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 6, length 53 :
% 0.20/0.44 % SZS output start Refutation
% 0.20/0.44 1[0:Inp] || -> member(u,singleton_set(u))*.
% 0.20/0.44 2[0:Inp] || member(u,singleton_set(v))* -> equal(u,v).
% 0.20/0.44 3[0:Inp] || -> member(u,unordered_pair(u,v))*.
% 0.20/0.44 4[0:Inp] || -> member(u,unordered_pair(v,u))*.
% 0.20/0.44 5[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 0.20/0.44 6[0:Inp] || -> equal(unordered_pair(singleton_set(u),unordered_pair(u,v)),ordered_pair(u,v))**.
% 0.20/0.44 7[0:Inp] || -> equal(ordered_pair(m2,r2),ordered_pair(m1,r1))**.
% 0.20/0.44 8[0:Inp] || equal(r2,r1)** -> .
% 0.20/0.44 11[0:Res:5.2,8.0] || member(r2,unordered_pair(u,r1))* -> equal(r2,u).
% 0.20/0.44 14[0:Res:5.2,8.0] || member(r1,unordered_pair(u,r2))* -> equal(r1,u).
% 0.20/0.44 15[0:Res:11.1,8.0] || member(r2,unordered_pair(r1,r1))* -> .
% 0.20/0.44 25[0:SpR:6.0,4.0] || -> member(unordered_pair(u,v),ordered_pair(u,v))*.
% 0.20/0.44 26[0:SpR:6.0,3.0] || -> member(singleton_set(u),ordered_pair(u,v))*.
% 0.20/0.44 29[0:SpR:7.0,26.0] || -> member(singleton_set(m2),ordered_pair(m1,r1))*.
% 0.20/0.44 30[0:SpR:7.0,25.0] || -> member(unordered_pair(m2,r2),ordered_pair(m1,r1))*.
% 0.20/0.44 32[0:SpL:6.0,5.0] || member(u,ordered_pair(v,w))* -> equal(u,unordered_pair(v,w)) equal(u,singleton_set(v)).
% 0.20/0.44 56[0:Res:29.0,32.0] || -> equal(unordered_pair(m1,r1),singleton_set(m2))** equal(singleton_set(m2),singleton_set(m1)).
% 0.20/0.44 58[0:Res:30.0,32.0] || -> equal(unordered_pair(m2,r2),unordered_pair(m1,r1))** equal(unordered_pair(m2,r2),singleton_set(m1)).
% 0.20/0.44 62[1:Spt:56.1] || -> equal(singleton_set(m2),singleton_set(m1))**.
% 0.20/0.44 75[1:SpR:62.0,1.0] || -> member(m2,singleton_set(m1))*.
% 0.20/0.44 82[1:Res:75.0,2.0] || -> equal(m2,m1)**.
% 0.20/0.44 83[1:Rew:82.0,7.0] || -> equal(ordered_pair(m1,r2),ordered_pair(m1,r1))**.
% 0.20/0.44 87[1:Rew:82.0,58.0] || -> equal(unordered_pair(m1,r2),unordered_pair(m1,r1)) equal(unordered_pair(m2,r2),singleton_set(m1))**.
% 0.20/0.44 95[1:Rew:82.0,87.1] || -> equal(unordered_pair(m1,r2),unordered_pair(m1,r1))** equal(unordered_pair(m1,r2),singleton_set(m1)).
% 0.20/0.44 106[2:Spt:95.0] || -> equal(unordered_pair(m1,r2),unordered_pair(m1,r1))**.
% 0.20/0.44 110[2:SpR:106.0,4.0] || -> member(r2,unordered_pair(m1,r1))*.
% 0.20/0.44 117[2:SpL:106.0,14.0] || member(r1,unordered_pair(m1,r1))* -> equal(r1,m1).
% 0.20/0.44 119[2:MRR:117.0,4.0] || -> equal(r1,m1)**.
% 0.20/0.44 123[2:Rew:119.0,15.0] || member(r2,unordered_pair(m1,m1))* -> .
% 0.20/0.44 131[2:Rew:119.0,110.0] || -> member(r2,unordered_pair(m1,m1))*.
% 0.20/0.44 132[2:MRR:123.0,131.0] || -> .
% 0.20/0.44 139[2:Spt:132.0,95.0,106.0] || equal(unordered_pair(m1,r2),unordered_pair(m1,r1))** -> .
% 0.20/0.44 140[2:Spt:132.0,95.1] || -> equal(unordered_pair(m1,r2),singleton_set(m1))**.
% 0.20/0.44 142[2:Rew:140.0,139.0] || equal(unordered_pair(m1,r1),singleton_set(m1))** -> .
% 0.20/0.44 146[2:SpR:140.0,4.0] || -> member(r2,singleton_set(m1))*.
% 0.20/0.44 155[2:Res:146.0,2.0] || -> equal(r2,m1)**.
% 0.20/0.44 156[2:Rew:155.0,140.0] || -> equal(unordered_pair(m1,m1),singleton_set(m1))**.
% 0.20/0.44 163[2:Rew:155.0,83.0] || -> equal(ordered_pair(m1,r1),ordered_pair(m1,m1))**.
% 0.20/0.44 184[2:SpR:163.0,25.0] || -> member(unordered_pair(m1,r1),ordered_pair(m1,m1))*.
% 0.20/0.44 191[2:Res:184.0,32.0] || -> equal(unordered_pair(m1,r1),unordered_pair(m1,m1))** equal(unordered_pair(m1,r1),singleton_set(m1)).
% 0.20/0.44 192[2:Rew:156.0,191.0] || -> equal(unordered_pair(m1,r1),singleton_set(m1))** equal(unordered_pair(m1,r1),singleton_set(m1))**.
% 0.20/0.44 193[2:Obv:192.0] || -> equal(unordered_pair(m1,r1),singleton_set(m1))**.
% 0.20/0.44 194[2:MRR:193.0,142.0] || -> .
% 0.20/0.44 195[1:Spt:194.0,56.1,62.0] || equal(singleton_set(m2),singleton_set(m1))** -> .
% 0.20/0.44 196[1:Spt:194.0,56.0] || -> equal(unordered_pair(m1,r1),singleton_set(m2))**.
% 0.20/0.44 198[1:SpR:196.0,4.0] || -> member(r1,singleton_set(m2))*.
% 0.20/0.44 199[1:SpR:196.0,3.0] || -> member(m1,singleton_set(m2))*.
% 0.20/0.44 205[1:Res:198.0,2.0] || -> equal(m2,r1)**.
% 0.20/0.44 209[1:Rew:205.0,195.0] || equal(singleton_set(r1),singleton_set(m1))** -> .
% 0.20/0.44 212[1:Rew:205.0,199.0] || -> member(m1,singleton_set(r1))*.
% 0.20/0.44 227[1:Res:212.0,2.0] || -> equal(r1,m1)**.
% 0.20/0.44 229[1:Rew:227.0,209.0] || equal(singleton_set(m1),singleton_set(m1))* -> .
% 0.20/0.44 253[1:Obv:229.0] || -> .
% 0.20/0.44 % SZS output end Refutation
% 0.20/0.44 Formulae used in the proof : singleton_1 singleton_2 unordered_pair_1 unordered_pair_2 unordered_pair_3 ordered_pair equal_ordered_pairs prove_second_components_equal
% 0.20/0.44
%------------------------------------------------------------------------------