%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP618+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:24:10 AM UTC 2026
% Result : Theorem 65.92s 9.52s
% Output : CNFRefutation 65.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP618+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:05:08 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.92/9.52 % SZS status Theorem for theBenchmark.p
% 65.92/9.52 % SZS output start CNFRefutation for theBenchmark.p
% 65.92/9.52 fof(l1_autgroup, axiom, ! [X0] : (((~'v3$ustruct$u0'(X0) & ('v1$ugroup$u1'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0))))) => ! [X1] : (('m1$ugroup$u2'(X1,X0) => (! [X2] : (('m1$usubset$u1'(X2,'u1$ustruct$u0'(X0)) => ! [X3] : (('m1$usubset$u1'(X3,'u1$ustruct$u0'(X0)) => ('m1$usubset$u1'(X3,'u1$ustruct$u0'(X1)) => 'r1$urlvect$u1'(X1,'k2$ugroup$u3'(X0,X3,X2))))))) => 'v1$ugroup$u3'(X1,X0))))))).
% 65.92/9.52 fof(l2_autgroup, axiom, ! [X0] : (((~'v3$ustruct$u0'(X0) & ('v1$ugroup$u1'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0))))) => ! [X1] : (('m1$ugroup$u2'(X1,X0) => ('v1$ugroup$u3'(X1,X0) => ! [X2] : (('m1$usubset$u1'(X2,'u1$ustruct$u0'(X0)) => ! [X3] : (('m1$usubset$u1'(X3,'u1$ustruct$u0'(X0)) => ('m1$usubset$u1'(X3,'u1$ustruct$u0'(X1)) => 'r1$urlvect$u1'(X1,'k2$ugroup$u3'(X0,X3,X2))))))))))))).
% 65.92/9.52 fof(t1_autgroup, conjecture, ! [X0] : (((~'v3$ustruct$u0'(X0) & ('v1$ugroup$u1'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0))))) => ! [X1] : (('m1$ugroup$u2'(X1,X0) => (! [X2] : (('m1$usubset$u1'(X2,'u1$ustruct$u0'(X0)) => ! [X3] : (('m1$usubset$u1'(X3,'u1$ustruct$u0'(X0)) => ('m1$usubset$u1'(X3,'u1$ustruct$u0'(X1)) => 'r1$urlvect$u1'(X1,'k2$ugroup$u3'(X0,X3,X2))))))) <=> 'v1$ugroup$u3'(X1,X0))))))).
% 65.92/9.52 fof(negated_conjecture, negated_conjecture, ~! [X0] : (((~'v3$ustruct$u0'(X0) & ('v1$ugroup$u1'(X0) & ('v3$ugroup$u1'(X0) & ('v4$ugroup$u1'(X0) & 'l1$ugroup$u1'(X0))))) => ! [X1] : (('m1$ugroup$u2'(X1,X0) => (! [X2] : (('m1$usubset$u1'(X2,'u1$ustruct$u0'(X0)) => ! [X3] : (('m1$usubset$u1'(X3,'u1$ustruct$u0'(X0)) => ('m1$usubset$u1'(X3,'u1$ustruct$u0'(X1)) => 'r1$urlvect$u1'(X1,'k2$ugroup$u3'(X0,X3,X2))))))) <=> 'v1$ugroup$u3'(X1,X0)))))), inference(negate_conjecture, [status(cth)], [t1_autgroup])).
% 65.92/9.52 cnf(c0, plain, ~'v1$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | 'm1$usubset$u1'(sK2(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$ugroup$u2'(X1,X0) | ~'v3$ugroup$u1'(X0) | ~'l1$ugroup$u1'(X0) | 'v1$ugroup$u3'(X1,X0) | ~'v4$ugroup$u1'(X0), inference(clausification, [status(esa)], [l1_autgroup])).
% 65.92/9.52 cnf(c1, plain, ~'v1$ugroup$u1'(X0) | 'm1$usubset$u1'(sK3(X0,X1),'u1$ustruct$u0'(X0)) | 'v3$ustruct$u0'(X0) | ~'m1$ugroup$u2'(X1,X0) | ~'v3$ugroup$u1'(X0) | ~'l1$ugroup$u1'(X0) | 'v1$ugroup$u3'(X1,X0) | ~'v4$ugroup$u1'(X0), inference(clausification, [status(esa)], [l1_autgroup])).
% 65.92/9.52 cnf(c2, plain, ~'v1$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'm1$usubset$u1'(sK3(X0,X1),'u1$ustruct$u0'(X1)) | ~'v3$ugroup$u1'(X0) | ~'l1$ugroup$u1'(X0) | 'v1$ugroup$u3'(X1,X0) | ~'v4$ugroup$u1'(X0), inference(clausification, [status(esa)], [l1_autgroup])).
% 65.92/9.52 cnf(c3, plain, ~'v1$ugroup$u1'(X0) | 'v3$ustruct$u0'(X0) | ~'r1$urlvect$u1'(X1,'k2$ugroup$u3'(X0,sK3(X0,X1),sK2(X0,X1))) | ~'m1$ugroup$u2'(X1,X0) | ~'v3$ugroup$u1'(X0) | ~'l1$ugroup$u1'(X0) | 'v1$ugroup$u3'(X1,X0) | ~'v4$ugroup$u1'(X0), inference(clausification, [status(esa)], [l1_autgroup])).
% 65.92/9.52 cnf(c4, plain, ~'m1$usubset$u1'(X0,'u1$ustruct$u0'(X1)) | ~'v1$ugroup$u1'(X1) | 'r1$urlvect$u1'(X2,'k2$ugroup$u3'(X1,X0,X3)) | ~'m1$ugroup$u2'(X2,X1) | ~'v1$ugroup$u3'(X2,X1) | ~'v4$ugroup$u1'(X1) | 'v3$ustruct$u0'(X1) | ~'m1$usubset$u1'(X3,'u1$ustruct$u0'(X1)) | ~'l1$ugroup$u1'(X1) | ~'v3$ugroup$u1'(X1) | ~'m1$usubset$u1'(X0,'u1$ustruct$u0'(X2)), inference(clausification, [status(esa)], [l2_autgroup])).
% 65.92/9.52 cnf(c449, plain, ~'v3$ustruct$u0'(sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c450, plain, 'v1$ugroup$u1'(sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c451, plain, 'v3$ugroup$u1'(sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c452, plain, 'v4$ugroup$u1'(sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c453, plain, 'l1$ugroup$u1'(sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c454, plain, 'm1$ugroup$u2'(sK756,sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c456, plain, X0(sK755,sK756) | 'v1$ugroup$u3'(sK756,sK755), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c457, plain, ~'v1$ugroup$u3'(sK756,sK755) | ~X0(sK755,sK756), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c459, plain, ~'m1$usubset$u1'(X0,'u1$ustruct$u0'(X1)) | ~X2(X1,X3) | 'r1$urlvect$u1'(X3,'k2$ugroup$u3'(X1,X0,X4)) | ~'m1$usubset$u1'(X4,'u1$ustruct$u0'(X1)) | ~'m1$usubset$u1'(X0,'u1$ustruct$u0'(X3)), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c460, plain, X0(X1,X2) | 'm1$usubset$u1'(sK759(X1,X2),'u1$ustruct$u0'(X1)), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c461, plain, X0(X1,X2) | 'm1$usubset$u1'(sK760(X1,X2),'u1$ustruct$u0'(X1)), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c462, plain, X0(X1,X2) | 'm1$usubset$u1'(sK760(X1,X2),'u1$ustruct$u0'(X2)), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(c463, plain, X0(X1,X2) | ~'r1$urlvect$u1'(X2,'k2$ugroup$u3'(X1,sK760(X1,X2),sK759(X1,X2))), inference(clausification, [status(esa)], [negated_conjecture])).
% 65.92/9.52 cnf(d0, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0) | ~'m1$usubset$u1'(sK3(X0,X1),'u1$ustruct$u0'(X1)) | ~'m1$usubset$u1'(sK3(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$usubset$u1'(sK2(X0,X1),'u1$ustruct$u0'(X0)) | ~'Ts754'(X0,X1), inference(resolution, [status(thm)], [c3,c459])).
% 65.92/9.52 cnf(d1, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | ~'m1$usubset$u1'(sK2(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$usubset$u1'(sK3(X0,X1),'u1$ustruct$u0'(X1)) | 'v3$ustruct$u0'(X0) | ~'Ts754'(X0,X1) | ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0), inference(resolution, [status(thm)], [d0,c1])).
% 65.92/9.52 cnf(d2, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | ~'m1$usubset$u1'(sK2(X0,X1),'u1$ustruct$u0'(X0)) | 'v3$ustruct$u0'(X0) | ~'Ts754'(X0,X1) | ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0), inference(resolution, [status(thm)], [d1,c2])).
% 65.92/9.52 cnf(d3, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0) | ~'Ts754'(X0,X1) | ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | 'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0), inference(resolution, [status(thm)], [d2,c0])).
% 65.92/9.52 cnf(d4, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v1$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755) | 'v3$ustruct$u0'(sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [d3,c456])).
% 65.92/9.52 cnf(d5, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v1$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c449,d4])).
% 65.92/9.52 cnf(d6, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c450,d5])).
% 65.92/9.52 cnf(d7, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c451,d6])).
% 65.92/9.52 cnf(d8, plain, ~'l1$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c452,d7])).
% 65.92/9.52 cnf(d9, plain, ~'m1$ugroup$u2'(sK756,sK755) | 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c453,d8])).
% 65.92/9.52 cnf(d10, plain, 'v1$ugroup$u3'(sK756,sK755), inference(resolution, [status(thm)], [c454,d9])).
% 65.92/9.52 cnf(d11, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | ~'v1$ugroup$u3'(X1,X0) | ~'m1$usubset$u1'(sK759(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$usubset$u1'(sK760(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$usubset$u1'(sK760(X0,X1),'u1$ustruct$u0'(X1)) | 'v3$ustruct$u0'(X0) | 'Ts754'(X0,X1), inference(resolution, [status(thm)], [c4,c463])).
% 65.92/9.52 cnf(d12, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | ~'v1$ugroup$u3'(X1,X0) | ~'m1$usubset$u1'(sK759(X0,X1),'u1$ustruct$u0'(X0)) | ~'m1$usubset$u1'(sK760(X0,X1),'u1$ustruct$u0'(X1)) | 'v3$ustruct$u0'(X0) | 'Ts754'(X0,X1) | 'Ts754'(X0,X1), inference(resolution, [status(thm)], [d11,c461])).
% 65.92/9.52 cnf(d13, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | ~'v1$ugroup$u3'(X1,X0) | ~'m1$usubset$u1'(sK759(X0,X1),'u1$ustruct$u0'(X0)) | 'v3$ustruct$u0'(X0) | 'Ts754'(X0,X1) | 'Ts754'(X0,X1), inference(resolution, [status(thm)], [d12,c462])).
% 65.92/9.52 cnf(d14, plain, ~'l1$ugroup$u1'(X0) | ~'v4$ugroup$u1'(X0) | ~'v1$ugroup$u1'(X0) | ~'v3$ugroup$u1'(X0) | ~'m1$ugroup$u2'(X1,X0) | ~'v1$ugroup$u3'(X1,X0) | 'v3$ustruct$u0'(X0) | 'Ts754'(X0,X1) | 'Ts754'(X0,X1), inference(resolution, [status(thm)], [d13,c460])).
% 65.92/9.52 cnf(d15, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v1$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'v3$ustruct$u0'(sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [d14,d10])).
% 65.92/9.52 cnf(d16, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v1$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c449,d15])).
% 65.92/9.52 cnf(d17, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'v3$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c450,d16])).
% 65.92/9.52 cnf(d18, plain, ~'l1$ugroup$u1'(sK755) | ~'v4$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c451,d17])).
% 65.92/9.52 cnf(d19, plain, ~'l1$ugroup$u1'(sK755) | ~'m1$ugroup$u2'(sK756,sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c452,d18])).
% 65.92/9.52 cnf(d20, plain, ~'m1$ugroup$u2'(sK756,sK755) | 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c453,d19])).
% 65.92/9.52 cnf(d21, plain, 'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [c454,d20])).
% 65.92/9.52 cnf(d22, plain, ~'Ts754'(sK755,sK756), inference(resolution, [status(thm)], [d10,c457])).
% 65.92/9.52 cnf(d23, plain, $false, inference(resolution, [status(thm)], [d22,d21])).
% 65.92/9.52 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------