%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:24:16 AM UTC 2026
% Result : Theorem 14.45s 7.29s
% Output : CNFRefutation 14.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP639+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 15:22:45 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.45/7.29 % SZS status Theorem for theBenchmark.p
% 14.45/7.29 % SZS output start CNFRefutation for theBenchmark.p
% 14.45/7.29 fof(cc1_relset_1, axiom, ! [X0] : ! [X1] : ! [X2] : (('m1$usubset$u1'(X2,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X0,X1))) => 'v1$urelat$u1'(X2)))).
% 14.45/7.29 fof(d5_group_4, axiom, ! [X0] : (((~'v3$ustruct$u0'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0)))) => ! [X1] : (('m1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) => ! [X2] : ((('v1$ugroup$u1'(X2) & 'm1$ugroup$u2'(X2,X0)) => (X2 = 'k5$ugroup$u4'(X0,X1) <=> ('r1$utarski'(X1,'u1$ustruct$u0'(X2)) & ! [X3] : ((('v1$ugroup$u1'(X3) & 'm1$ugroup$u2'(X3,X0)) => ('r1$utarski'(X1,'u1$ustruct$u0'(X3)) => 'm1$ugroup$u2'(X2,X3))))))))))))).
% 14.45/7.29 fof(dt_k5_group_4, axiom, ! [X0] : ! [X1] : (((~'v3$ustruct$u0'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & ('l1$ugroup$u1'(X0) & 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))))))) => ('v1$ugroup$u1'('k5$ugroup$u4'(X0,X1)) & 'm1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0))))).
% 14.45/7.29 fof(dt_m2_relset_1, axiom, ! [X0] : ! [X1] : ! [X2] : (('m2$urelset$u1'(X2,X0,X1) => 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X0,X1)))))).
% 14.45/7.29 fof(redefinition_k2_funct_2, axiom, ! [X0] : ! [X1] : ! [X2] : ! [X3] : ((('v1$ufunct$u1'(X2) & ('v1$ufunct$u2'(X2,X0,X1) & 'm1$urelset$u1'(X2,X0,X1))) => 'k2$ufunct$u2'(X0,X1,X2,X3) = 'k9$urelat$u1'(X2,X3)))).
% 14.45/7.29 fof(redefinition_m2_relset_1, axiom, ! [X0] : ! [X1] : ! [X2] : (('m2$urelset$u1'(X2,X0,X1) <=> 'm1$urelset$u1'(X2,X0,X1)))).
% 14.45/7.29 fof(t156_relat_1, axiom, ! [X0] : ! [X1] : ! [X2] : (('v1$urelat$u1'(X2) => ('r1$utarski'(X0,X1) => 'r1$utarski'('k9$urelat$u1'(X2,X0),'k9$urelat$u1'(X2,X1)))))).
% 14.45/7.29 fof(t12_latsubgr, conjecture, ! [X0] : (((~'v3$ustruct$u0'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0)))) => ! [X1] : (((~'v3$ustruct$u0'(X1) & ('v3$ugroup$u1'(X1) & ('v4$ugroup$u1'(X1) & 'l1$ugroup$u1'(X1)))) => ! [X2] : ((('v1$ufunct$u1'(X2) & ('v1$ufunct$u2'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1)) & 'm2$urelset$u1'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1)))) => ! [X3] : (('m1$usubset$u1'(X3,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) => 'r1$utarski'('k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,X3),'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'('k5$ugroup$u4'(X0,X3))))))))))))).
% 14.45/7.29 fof(negated_conjecture, negated_conjecture, ~! [X0] : (((~'v3$ustruct$u0'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0)))) => ! [X1] : (((~'v3$ustruct$u0'(X1) & ('v3$ugroup$u1'(X1) & ('v4$ugroup$u1'(X1) & 'l1$ugroup$u1'(X1)))) => ! [X2] : ((('v1$ufunct$u1'(X2) & ('v1$ufunct$u2'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1)) & 'm2$urelset$u1'(X2,'u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1)))) => ! [X3] : (('m1$usubset$u1'(X3,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) => 'r1$utarski'('k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,X3),'k2$ufunct$u2'('u1$ustruct$u0'(X0),'u1$ustruct$u0'(X1),X2,'u1$ustruct$u0'('k5$ugroup$u4'(X0,X3)))))))))))), inference(negate_conjecture, [status(cth)], [t12_latsubgr])).
% 14.45/7.29 cnf(c4, plain, ~'m1$usubset$u1'(X0,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X1,X2))) | 'v1$urelat$u1'(X0), inference(clausification, [status(esa)], [cc1_relset_1])).
% 14.45/7.29 cnf(c12, plain, ~'v4$ugroup$u1'(X0) | X1 != 'k5$ugroup$u4'(X0,X2) | ~'v1$ugroup$u1'(X1) | ~'l1$ugroup$u1'(X0) | ~'m1$usubset$u1'(X2,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) | X3(X0,X2,X1) | ~'m1$ugroup$u2'(X1,X0) | ~'v3$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0), inference(clausification, [status(esa)], [d5_group_4])).
% 14.45/7.29 cnf(c14, plain, ~X0(X1,X2,X3) | 'r1$utarski'(X2,'u1$ustruct$u0'(X3)), inference(clausification, [status(esa)], [d5_group_4])).
% 14.45/7.29 cnf(c23, plain, ~'v3$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | ~'l1$ugroup$u1'(X0) | 'v1$ugroup$u1'('k5$ugroup$u4'(X0,X1)) | ~'v4$ugroup$u1'(X0) | ~'m1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))), inference(clausification, [status(esa)], [dt_k5_group_4])).
% 14.45/7.29 cnf(c24, plain, 'm1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0) | ~'v3$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'m1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))), inference(clausification, [status(esa)], [dt_k5_group_4])).
% 14.45/7.29 cnf(c29, plain, ~'m2$urelset$u1'(X0,X1,X2) | 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k2$uzfmisc$u1'(X1,X2))), inference(clausification, [status(esa)], [dt_m2_relset_1])).
% 14.45/7.29 cnf(c62, plain, ~'v1$ufunct$u1'(X0) | ~'v1$ufunct$u2'(X0,X1,X2) | ~'m1$urelset$u1'(X0,X1,X2) | 'k2$ufunct$u2'(X1,X2,X0,X3) = 'k9$urelat$u1'(X0,X3), inference(clausification, [status(esa)], [redefinition_k2_funct_2])).
% 14.45/7.29 cnf(c63, plain, ~'m2$urelset$u1'(X0,X1,X2) | 'm1$urelset$u1'(X0,X1,X2), inference(clausification, [status(esa)], [redefinition_m2_relset_1])).
% 14.45/7.29 cnf(c66, plain, ~'v1$urelat$u1'(X0) | ~'r1$utarski'(X1,X2) | 'r1$utarski'('k9$urelat$u1'(X0,X1),'k9$urelat$u1'(X0,X2)), inference(clausification, [status(esa)], [t156_relat_1])).
% 14.45/7.29 cnf(c76, plain, ~'v3$ustruct$u0'(sK100), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c77, plain, 'v3$ugroup$u1'(sK100), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c78, plain, 'v4$ugroup$u1'(sK100), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c79, plain, 'l1$ugroup$u1'(sK100), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c84, plain, 'v1$ufunct$u1'(sK102), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c85, plain, 'v1$ufunct$u2'(sK102,'u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101)), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c86, plain, 'm2$urelset$u1'(sK102,'u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101)), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c87, plain, 'm1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(c88, plain, ~'r1$utarski'('k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,sK103),'k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103)))), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.45/7.29 cnf(d0, plain, ~'l1$ugroup$u1'(sK100) | 'm1$ugroup$u2'('k5$ugroup$u4'(sK100,sK103),sK100) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100) | 'v3$ustruct$u0'(sK100), inference(resolution, [status(thm)], [c24,c87])).
% 14.45/7.29 cnf(d1, plain, ~'l1$ugroup$u1'(sK100) | 'm1$ugroup$u2'('k5$ugroup$u4'(sK100,sK103),sK100) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100), inference(resolution, [status(thm)], [c76,d0])).
% 14.45/7.29 cnf(d2, plain, ~'l1$ugroup$u1'(sK100) | 'm1$ugroup$u2'('k5$ugroup$u4'(sK100,sK103),sK100) | ~'v4$ugroup$u1'(sK100), inference(resolution, [status(thm)], [c77,d1])).
% 14.45/7.29 cnf(d3, plain, ~'l1$ugroup$u1'(sK100) | 'm1$ugroup$u2'('k5$ugroup$u4'(sK100,sK103),sK100), inference(resolution, [status(thm)], [c78,d2])).
% 14.45/7.29 cnf(d4, plain, 'm1$ugroup$u2'('k5$ugroup$u4'(sK100,sK103),sK100), inference(resolution, [status(thm)], [c79,d3])).
% 14.45/7.29 cnf(d5, plain, ~'l1$ugroup$u1'(X0) | ~'v1$ugroup$u1'('k5$ugroup$u4'(X0,X1)) | ~'m1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) | ~'m1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0) | ~'v4$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | 'Ts15'(X0,X1,'k5$ugroup$u4'(X0,X1)) | 'v3$ustruct$u0'(X0), inference(equality_resolution, [status(thm)], [c12])).
% 14.45/7.29 cnf(d6, plain, ~'l1$ugroup$u1'(X0) | ~'v1$ugroup$u1'('k5$ugroup$u4'(X0,X1)) | ~'m1$usubset$u1'(X1,'k1$uzfmisc$u1'('u1$ustruct$u0'(X0))) | ~'m1$ugroup$u2'('k5$ugroup$u4'(X0,X1),X0) | ~'v4$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | 'r1$utarski'(X1,'u1$ustruct$u0'('k5$ugroup$u4'(X0,X1))), inference(resolution, [status(thm)], [d5,c14])).
% 14.45/7.29 cnf(d7, plain, ~'l1$ugroup$u1'(sK100) | ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'m1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100) | 'v3$ustruct$u0'(sK100) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [d6,d4])).
% 14.45/7.29 cnf(d8, plain, ~'l1$ugroup$u1'(sK100) | ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'m1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [c76,d7])).
% 14.45/7.29 cnf(d9, plain, ~'l1$ugroup$u1'(sK100) | ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'m1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))) | ~'v4$ugroup$u1'(sK100) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [c77,d8])).
% 14.45/7.29 cnf(d10, plain, ~'l1$ugroup$u1'(sK100) | ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'m1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [c78,d9])).
% 14.45/7.29 cnf(d11, plain, ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'m1$usubset$u1'(sK103,'k1$uzfmisc$u1'('u1$ustruct$u0'(sK100))) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [c79,d10])).
% 14.45/7.29 cnf(d12, plain, ~'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [c87,d11])).
% 14.45/7.29 cnf(d13, plain, ~'l1$ugroup$u1'(sK100) | 'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100) | 'v3$ustruct$u0'(sK100), inference(resolution, [status(thm)], [c23,c87])).
% 14.45/7.29 cnf(d14, plain, ~'l1$ugroup$u1'(sK100) | 'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'v4$ugroup$u1'(sK100) | ~'v3$ugroup$u1'(sK100), inference(resolution, [status(thm)], [c76,d13])).
% 14.45/7.29 cnf(d15, plain, ~'l1$ugroup$u1'(sK100) | 'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)) | ~'v4$ugroup$u1'(sK100), inference(resolution, [status(thm)], [c77,d14])).
% 14.45/7.29 cnf(d16, plain, ~'l1$ugroup$u1'(sK100) | 'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)), inference(resolution, [status(thm)], [c78,d15])).
% 14.45/7.29 cnf(d17, plain, 'v1$ugroup$u1'('k5$ugroup$u4'(sK100,sK103)), inference(resolution, [status(thm)], [c79,d16])).
% 14.45/7.29 cnf(d18, plain, 'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [d17,d12])).
% 14.45/7.29 cnf(d19, plain, 'k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,X0) = 'k9$urelat$u1'(sK102,X0) | ~'v1$ufunct$u1'(sK102) | ~'m1$urelset$u1'(sK102,'u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101)), inference(resolution, [status(thm)], [c62,c85])).
% 14.45/7.29 cnf(d20, plain, 'k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,X0) = 'k9$urelat$u1'(sK102,X0) | ~'m1$urelset$u1'(sK102,'u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101)), inference(resolution, [status(thm)], [c84,d19])).
% 14.45/7.29 cnf(d21, plain, 'm1$urelset$u1'(sK102,'u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101)), inference(resolution, [status(thm)], [c63,c86])).
% 14.45/7.29 cnf(d22, plain, 'k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,X0) = 'k9$urelat$u1'(sK102,X0), inference(resolution, [status(thm)], [d21,d20])).
% 14.45/7.29 cnf(d23, plain, ~'r1$utarski'('k9$urelat$u1'(sK102,sK103),'k2$ufunct$u2'('u1$ustruct$u0'(sK100),'u1$ustruct$u0'(sK101),sK102,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103)))), inference(demodulation, [status(thm)], [c88,d22])).
% 14.45/7.29 cnf(d24, plain, ~'r1$utarski'('k9$urelat$u1'(sK102,sK103),'k9$urelat$u1'(sK102,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103)))), inference(demodulation, [status(thm)], [d23,d22])).
% 14.45/7.29 cnf(d25, plain, ~'v1$urelat$u1'(sK102) | ~'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [d24,c66])).
% 14.45/7.29 cnf(d26, plain, ~'m2$urelset$u1'(X0,X1,X2) | 'v1$urelat$u1'(X0), inference(resolution, [status(thm)], [c29,c4])).
% 14.45/7.29 cnf(d27, plain, 'v1$urelat$u1'(sK102), inference(resolution, [status(thm)], [d26,c86])).
% 14.45/7.29 cnf(d28, plain, ~'r1$utarski'(sK103,'u1$ustruct$u0'('k5$ugroup$u4'(sK100,sK103))), inference(resolution, [status(thm)], [d27,d25])).
% 14.45/7.29 cnf(d29, plain, $false, inference(resolution, [status(thm)], [d28,d18])).
% 14.45/7.29 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------