TSTP Solution File: SET919+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:29:48 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET919+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 18:38:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 754 clauses, backtracked 42 clauses, performed 4 splits and kept 369 clauses.
% 0.37/0.55 SPASS allocated 85785 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.20 on the problem.
% 0.37/0.55 0:00:00.03 for the input.
% 0.37/0.55 0:00:00.04 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.01 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.09 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 6, length 78 :
% 0.37/0.55 % SZS output start Refutation
% 0.37/0.55 2[0:Inp] || -> in(skc5,skc6)*.
% 0.37/0.55 5[0:Inp] || in(skc7,skc6)* -> equal(skc7,skc5).
% 0.37/0.55 6[0:Inp] || -> equal(unordered_pair(u,v),unordered_pair(v,u))*.
% 0.37/0.55 7[0:Inp] || -> equal(set_intersection2(u,v),set_intersection2(v,u))*.
% 0.37/0.55 9[0:Inp] || equal(set_intersection2(unordered_pair(skc5,skc7),skc6),singleton(skc5))** -> .
% 0.37/0.55 10[0:Inp] || -> equal(skf3(u,v),u) in(skf3(u,v),v)*.
% 0.37/0.55 11[0:Inp] || in(u,v)* equal(v,singleton(w))*+ -> equal(u,w)*.
% 0.37/0.55 12[0:Inp] || equal(u,v)* equal(w,singleton(v))*+ -> in(u,w)*.
% 0.37/0.55 14[0:Inp] || equal(u,v)* equal(w,unordered_pair(x,v))*+ -> in(u,w)*.
% 0.37/0.55 17[0:Inp] || equal(skf3(u,v),u) in(skf3(u,v),v)* -> equal(v,singleton(u)).
% 0.37/0.55 18[0:Inp] || in(u,v)* equal(v,unordered_pair(w,x))*+ -> equal(u,x)* equal(u,w)*.
% 0.37/0.55 20[0:Inp] || -> equal(u,set_intersection2(v,w)) in(skf5(w,v,u),u)* in(skf5(w,v,u),v)*.
% 0.37/0.55 21[0:Inp] || -> equal(u,set_intersection2(v,w)) in(skf5(w,v,u),u)* in(skf5(w,v,u),w)*.
% 0.37/0.55 25[0:Inp] || in(skf5(u,v,w),u)*+ in(skf5(u,v,w),v)* in(skf5(u,v,w),w)* -> equal(w,set_intersection2(v,u)).
% 0.37/0.55 26[0:Rew:7.0,9.0] || equal(set_intersection2(skc6,unordered_pair(skc5,skc7)),singleton(skc5))** -> .
% 0.37/0.55 42[0:Res:25.3,26.0] || in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 43[0:Res:20.2,26.0] || -> in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 44[0:Res:21.2,26.0] || -> in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))*.
% 0.37/0.55 49[1:Spt:5.1] || -> equal(skc7,skc5)**.
% 0.37/0.55 53[1:Rew:49.0,26.0] || equal(set_intersection2(skc6,unordered_pair(skc5,skc5)),singleton(skc5))** -> .
% 0.37/0.55 54[1:Rew:49.0,42.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 55[1:Rew:49.0,43.0] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 56[1:Rew:49.0,44.0] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))*.
% 0.37/0.55 57[1:Rew:49.0,55.1] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 58[1:Rew:49.0,56.1] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),unordered_pair(skc5,skc5))*.
% 0.37/0.55 61[1:Rew:49.0,54.2,49.0,54.1] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),unordered_pair(skc5,skc5))* -> .
% 0.37/0.55 91[0:EqR:12.1] || equal(u,v) -> in(u,singleton(v))*.
% 0.37/0.55 95[0:EqR:11.1] || in(u,singleton(v))* -> equal(u,v).
% 0.37/0.55 98[0:Res:10.1,95.0] || -> equal(skf3(u,singleton(v)),u)** equal(skf3(u,singleton(v)),v)**.
% 0.37/0.55 105[0:SpR:98.1,10.1] || -> equal(skf3(u,singleton(v)),u)** equal(skf3(u,singleton(v)),u)** in(v,singleton(v))*.
% 0.37/0.55 111[0:Obv:105.0] || -> equal(skf3(u,singleton(v)),u)** in(v,singleton(v))*.
% 0.37/0.55 122[0:EqR:14.1] || equal(u,v) -> in(u,unordered_pair(w,v))*.
% 0.37/0.55 125[0:SpR:6.0,122.1] || equal(u,v) -> in(u,unordered_pair(v,w))*.
% 0.37/0.55 206[0:SpL:111.0,17.1] || equal(skf3(u,singleton(v)),u)** in(u,singleton(v)) -> in(v,singleton(v))* equal(singleton(v),singleton(u)).
% 0.37/0.55 213[0:Rew:111.0,206.0] || equal(u,u) in(u,singleton(v))* -> in(v,singleton(v))* equal(singleton(v),singleton(u)).
% 0.37/0.55 214[0:Obv:213.0] || in(u,singleton(v))*+ -> in(v,singleton(v))* equal(singleton(v),singleton(u)).
% 0.37/0.55 234[0:EqR:18.1] || in(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 0.37/0.55 352[0:Res:91.1,214.0] || equal(u,v) -> in(v,singleton(v))* equal(singleton(v),singleton(u))*.
% 0.37/0.55 362[0:MRR:352.2,12.1] || equal(u,v)*+ -> in(v,singleton(v))*.
% 0.37/0.55 371[0:EqR:362.0] || -> in(u,singleton(u))*.
% 0.37/0.55 609[2:Spt:57.0] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6)*.
% 0.37/0.55 610[2:MRR:61.0,609.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5)) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),unordered_pair(skc5,skc5))* -> .
% 0.37/0.55 682[3:Spt:58.0] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 683[3:MRR:610.0,682.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),unordered_pair(skc5,skc5))* -> .
% 0.37/0.55 693[3:Res:682.0,95.0] || -> equal(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc5)**.
% 0.37/0.55 718[3:Rew:693.0,683.0] || in(skc5,unordered_pair(skc5,skc5))* -> .
% 0.37/0.55 741[3:Res:125.1,718.0] || equal(skc5,skc5)* -> .
% 0.37/0.55 743[3:Obv:741.0] || -> .
% 0.37/0.55 744[3:Spt:743.0,58.0,682.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5))* -> .
% 0.37/0.55 745[3:Spt:743.0,58.1] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),unordered_pair(skc5,skc5))*.
% 0.37/0.55 754[3:Res:745.0,234.0] || -> equal(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc5)** equal(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc5)**.
% 0.37/0.55 756[3:Res:745.0,25.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5))* -> equal(set_intersection2(skc6,unordered_pair(skc5,skc5)),singleton(skc5)).
% 0.37/0.55 757[3:Obv:754.0] || -> equal(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc5)**.
% 0.37/0.55 789[3:Rew:757.0,756.1,757.0,756.0] || in(skc5,skc6) in(skc5,singleton(skc5)) -> equal(set_intersection2(skc6,unordered_pair(skc5,skc5)),singleton(skc5))**.
% 0.37/0.55 790[3:MRR:789.0,789.1,789.2,2.0,371.0,53.0] || -> .
% 0.37/0.55 796[2:Spt:790.0,57.0,609.0] || in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc6)* -> .
% 0.37/0.55 797[2:Spt:790.0,57.1] || -> in(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 806[2:Res:797.0,95.0] || -> equal(skf5(unordered_pair(skc5,skc5),skc6,singleton(skc5)),skc5)**.
% 0.37/0.55 810[2:Rew:806.0,796.0] || in(skc5,skc6)* -> .
% 0.37/0.55 811[2:MRR:810.0,2.0] || -> .
% 0.37/0.55 818[1:Spt:811.0,5.1,49.0] || equal(skc7,skc5)** -> .
% 0.37/0.55 819[1:Spt:811.0,5.0] || in(skc7,skc6)* -> .
% 0.37/0.55 821[2:Spt:43.1] || -> in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5))*.
% 0.37/0.55 822[2:MRR:42.1,821.0] || in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 829[2:Res:821.0,95.0] || -> equal(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc5)**.
% 0.37/0.55 833[2:Rew:829.0,822.0] || in(skc5,skc6) in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 838[2:Rew:829.0,833.1] || in(skc5,skc6) in(skc5,unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 839[2:MRR:838.0,2.0] || in(skc5,unordered_pair(skc5,skc7))* -> .
% 0.37/0.55 845[2:Res:125.1,839.0] || equal(skc5,skc5)* -> .
% 0.37/0.55 846[2:Obv:845.0] || -> .
% 0.37/0.55 847[2:Spt:846.0,43.1,821.0] || in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),singleton(skc5))* -> .
% 0.37/0.55 848[2:Spt:846.0,43.0] || -> in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc6)*.
% 0.37/0.55 849[2:MRR:44.0,847.0] || -> in(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),unordered_pair(skc5,skc7))*.
% 0.37/0.55 865[2:Res:91.1,847.0] || equal(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc5)** -> .
% 0.37/0.55 871[2:Res:849.0,234.0] || -> equal(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc7)** equal(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc5).
% 0.37/0.55 874[2:MRR:871.1,865.0] || -> equal(skf5(unordered_pair(skc5,skc7),skc6,singleton(skc5)),skc7)**.
% 0.37/0.55 875[2:Rew:874.0,848.0] || -> in(skc7,skc6)*.
% 0.37/0.55 886[2:MRR:875.0,819.0] || -> .
% 0.37/0.55 % SZS output end Refutation
% 0.37/0.55 Formulae used in the proof : t60_zfmisc_1 commutativity_k2_tarski commutativity_k3_xboole_0 d1_tarski idempotence_k3_xboole_0 d2_tarski d3_xboole_0
% 0.37/0.55
%------------------------------------------------------------------------------