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