TSTP Solution File: SET624+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 05:27:36 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET624+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 21:23:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 610 clauses, backtracked 19 clauses, performed 3 splits and kept 324 clauses.
% 0.19/0.49 SPASS allocated 85536 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.03 for the input.
% 0.19/0.49 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.04 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 10, length 50 :
% 0.19/0.49 % SZS output start Refutation
% 0.19/0.49 1[0:Inp] || -> equal(union(u,v),union(v,u))*.
% 0.19/0.49 2[0:Inp] || intersect(u,v)*+ -> intersect(v,u)*.
% 0.19/0.49 3[0:Inp] || member(u,v) -> member(u,union(v,w))*.
% 0.19/0.49 4[0:Inp] || member(u,v) -> member(u,union(w,v))*.
% 0.19/0.49 5[0:Inp] || intersect(u,v) -> member(skf2(v,u),u)*.
% 0.19/0.49 6[0:Inp] || intersect(u,v)*+ -> member(skf2(v,w),v)*.
% 0.19/0.49 7[0:Inp] || intersect(skc3,skc4) intersect(skc3,union(skc4,skc5))* -> .
% 0.19/0.49 8[0:Inp] || intersect(skc3,skc5) intersect(skc3,union(skc4,skc5))* -> .
% 0.19/0.49 9[0:Inp] || -> intersect(skc3,skc5) intersect(skc3,skc4) intersect(skc3,union(skc4,skc5))*.
% 0.19/0.49 10[0:Inp] || member(u,v)*+ member(u,w)* -> intersect(w,v)*.
% 0.19/0.49 13[0:Inp] || member(u,union(v,w))* -> member(u,v) member(u,w).
% 0.19/0.49 16[1:Spt:8.1] || intersect(skc3,union(skc4,skc5))* -> .
% 0.19/0.49 17[1:MRR:9.2,16.0] || -> intersect(skc3,skc5)* intersect(skc3,skc4).
% 0.19/0.49 24[1:Res:17.0,6.0] || -> intersect(skc3,skc4) member(skf2(skc5,u),skc5)*.
% 0.19/0.49 26[2:Spt:24.0] || -> intersect(skc3,skc4)*.
% 0.19/0.49 28[2:Res:26.0,2.0] || -> intersect(skc4,skc3)*.
% 0.19/0.49 29[2:Res:28.0,6.0] || -> member(skf2(skc3,u),skc3)*.
% 0.19/0.49 37[2:Res:29.0,10.0] || member(skf2(skc3,u),v)* -> intersect(v,skc3).
% 0.19/0.49 39[0:Res:3.1,10.0] || member(u,v)*+ member(u,w)* -> intersect(w,union(v,x))*.
% 0.19/0.49 49[2:Res:4.1,37.0] || member(skf2(skc3,u),v)*+ -> intersect(union(w,v),skc3)*.
% 0.19/0.49 59[0:Res:5.1,13.0] || intersect(union(u,v),w)+ -> member(skf2(w,union(u,v)),u)* member(skf2(w,union(u,v)),v)*.
% 0.19/0.49 118[2:Res:5.1,49.0] || intersect(u,skc3) -> intersect(union(v,u),skc3)*.
% 0.19/0.49 208[2:SpR:1.0,118.1] || intersect(u,skc3) -> intersect(union(u,v),skc3)*.
% 0.19/0.49 241[2:Res:208.1,2.0] || intersect(u,skc3) -> intersect(skc3,union(u,v))*.
% 0.19/0.49 250[2:Res:241.1,16.0] || intersect(skc4,skc3)* -> .
% 0.19/0.49 254[2:MRR:250.0,28.0] || -> .
% 0.19/0.49 255[2:Spt:254.0,24.0,26.0] || intersect(skc3,skc4)* -> .
% 0.19/0.49 256[2:Spt:254.0,24.1] || -> member(skf2(skc5,u),skc5)*.
% 0.19/0.49 257[2:MRR:17.1,255.0] || -> intersect(skc3,skc5)*.
% 0.19/0.49 261[2:Res:256.0,39.0] || member(skf2(skc5,u),v)*+ -> intersect(v,union(skc5,w))*.
% 0.19/0.49 294[2:Res:5.1,261.0] || intersect(u,skc5) -> intersect(u,union(skc5,v))*.
% 0.19/0.49 342[2:SpR:1.0,294.1] || intersect(u,skc5) -> intersect(u,union(v,skc5))*.
% 0.19/0.49 372[2:Res:342.1,16.0] || intersect(skc3,skc5)* -> .
% 0.19/0.49 377[2:MRR:372.0,257.0] || -> .
% 0.19/0.49 378[1:Spt:377.0,8.1,16.0] || -> intersect(skc3,union(skc4,skc5))*.
% 0.19/0.49 379[1:Spt:377.0,8.0] || intersect(skc3,skc5)* -> .
% 0.19/0.49 380[1:MRR:7.1,378.0] || intersect(skc3,skc4)* -> .
% 0.19/0.49 383[1:Res:378.0,2.0] || -> intersect(union(skc4,skc5),skc3)*.
% 0.19/0.49 385[1:Res:383.0,6.0] || -> member(skf2(skc3,u),skc3)*.
% 0.19/0.49 387[1:Res:383.0,59.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4) member(skf2(skc3,union(skc4,skc5)),skc5)*.
% 0.19/0.49 394[1:Res:385.0,10.0] || member(skf2(skc3,u),v)* -> intersect(v,skc3).
% 0.19/0.49 639[1:Res:387.1,394.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4)* intersect(skc5,skc3).
% 0.19/0.49 649[2:Spt:639.0] || -> member(skf2(skc3,union(skc4,skc5)),skc4)*.
% 0.19/0.49 654[2:Res:649.0,394.0] || -> intersect(skc4,skc3)*.
% 0.19/0.49 661[2:Res:654.0,2.0] || -> intersect(skc3,skc4)*.
% 0.19/0.49 662[2:MRR:661.0,380.0] || -> .
% 0.19/0.49 663[2:Spt:662.0,639.0,649.0] || member(skf2(skc3,union(skc4,skc5)),skc4)* -> .
% 0.19/0.49 664[2:Spt:662.0,639.1] || -> intersect(skc5,skc3)*.
% 0.19/0.49 675[2:Res:664.0,2.0] || -> intersect(skc3,skc5)*.
% 0.19/0.49 676[2:MRR:675.0,379.0] || -> .
% 0.19/0.49 % SZS output end Refutation
% 0.19/0.49 Formulae used in the proof : commutativity_of_union symmetry_of_intersect union_defn intersect_defn prove_intersect_with_union
% 0.19/0.49
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