%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET646+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:33:00 AM UTC 2026
% Result : Theorem 28.18s 7.09s
% Output : CNFRefutation 28.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:00:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.18/7.09 % SZS status Theorem for theBenchmark.p
% 28.18/7.09 % SZS output start CNFRefutation for theBenchmark.p
% 28.18/7.09 fof(p2, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => ! [X3] : (('ilf$utype'(X3,'set$utype') => (member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) <=> (member(X0,X2) & member(X1,X3)))))))))))).
% 28.18/7.09 fof(p3, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => (! [X2] : (('ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1))) => 'ilf$utype'(X2,'relation$utype'(X0,X1)))) & ! [X3] : (('ilf$utype'(X3,'relation$utype'(X0,X1)) => 'ilf$utype'(X3,'subset$utype'('cross$uproduct'(X0,X1))))))))))).
% 28.18/7.09 fof(p5, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => (X2 = singleton(X1) <=> ! [X3] : (('ilf$utype'(X3,'set$utype') => (member(X3,X2) <=> X3 = X1))))))))))).
% 28.18/7.09 fof(p12, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ('ilf$utype'(X1,'subset$utype'(X0)) <=> 'ilf$utype'(X1,'member$utype'('power$uset'(X0))))))))).
% 28.18/7.09 fof(p17, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => (member(X0,'power$uset'(X1)) <=> ! [X2] : (('ilf$utype'(X2,'set$utype') => (member(X2,X0) => member(X2,X1)))))))))).
% 28.18/7.09 fof(p18, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => (~empty('power$uset'(X0)) & 'ilf$utype'('power$uset'(X0),'set$utype'))))).
% 28.18/7.09 fof(p19, axiom, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (((~empty(X1) & 'ilf$utype'(X1,'set$utype')) => ('ilf$utype'(X0,'member$utype'(X1)) <=> member(X0,X1))))))).
% 28.18/7.09 fof(p25, axiom, ! [X0] : 'ilf$utype'(X0,'set$utype')).
% 28.18/7.09 fof(prove_relset_1_8, conjecture, ! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => ! [X3] : (('ilf$utype'(X3,'set$utype') => ((member(X2,X0) & member(X3,X1)) => 'ilf$utype'(singleton('ordered$upair'(X2,X3)),'relation$utype'(X0,X1)))))))))))).
% 28.18/7.09 fof(negated_conjecture, negated_conjecture, ~! [X0] : (('ilf$utype'(X0,'set$utype') => ! [X1] : (('ilf$utype'(X1,'set$utype') => ! [X2] : (('ilf$utype'(X2,'set$utype') => ! [X3] : (('ilf$utype'(X3,'set$utype') => ((member(X2,X0) & member(X3,X1)) => 'ilf$utype'(singleton('ordered$upair'(X2,X3)),'relation$utype'(X0,X1))))))))))), inference(negate_conjecture, [status(cth)], [prove_relset_1_8])).
% 28.18/7.09 cnf(c4, plain, ~member(X0,X1) | ~member(X2,X3) | ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | ~'ilf$utype'(X2,'set$utype') | member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3)) | ~'ilf$utype'(X3,'set$utype'), inference(clausification, [status(esa)], [p2])).
% 28.18/7.09 cnf(c5, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | ~'ilf$utype'(X2,'subset$utype'('cross$uproduct'(X0,X1))) | 'ilf$utype'(X2,'relation$utype'(X0,X1)), inference(clausification, [status(esa)], [p3])).
% 28.18/7.09 cnf(c8, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | X2 != singleton(X0) | ~'ilf$utype'(X2,'set$utype') | X3(X0,X2), inference(clausification, [status(esa)], [p5])).
% 28.18/7.09 cnf(c10, plain, ~X0(X1,X2) | ~'ilf$utype'(X3,'set$utype') | ~member(X3,X2) | X3 = X1, inference(clausification, [status(esa)], [p5])).
% 28.18/7.09 cnf(c25, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | 'ilf$utype'(X1,'subset$utype'(X0)) | ~'ilf$utype'(X1,'member$utype'('power$uset'(X0))), inference(clausification, [status(esa)], [p12])).
% 28.18/7.09 cnf(c43, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | member(X0,'power$uset'(X1)) | member(sK50(X0,X1),X0), inference(clausification, [status(esa)], [p17])).
% 28.18/7.09 cnf(c44, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | member(X0,'power$uset'(X1)) | ~member(sK50(X0,X1),X1), inference(clausification, [status(esa)], [p17])).
% 28.18/7.09 cnf(c45, plain, ~'ilf$utype'(X0,'set$utype') | ~empty('power$uset'(X0)), inference(clausification, [status(esa)], [p18])).
% 28.18/7.09 cnf(c48, plain, empty(X0) | 'ilf$utype'(X1,'member$utype'(X0)) | ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | ~member(X1,X0), inference(clausification, [status(esa)], [p19])).
% 28.18/7.09 cnf(c63, plain, 'ilf$utype'(X0,'set$utype'), inference(clausification, [status(esa)], [p25])).
% 28.18/7.09 cnf(c68, plain, member(sK74,sK72), inference(clausification, [status(esa)], [negated_conjecture])).
% 28.18/7.09 cnf(c69, plain, member(sK75,sK73), inference(clausification, [status(esa)], [negated_conjecture])).
% 28.18/7.09 cnf(c70, plain, ~'ilf$utype'(singleton('ordered$upair'(sK74,sK75)),'relation$utype'(sK72,sK73)), inference(clausification, [status(esa)], [negated_conjecture])).
% 28.18/7.09 cnf(d0, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(X1,'set$utype') | ~'ilf$utype'(X2,'set$utype') | ~member(X0,X1) | ~member(X2,X3) | member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3)), inference(resolution, [status(thm)], [c63,c4])).
% 28.18/7.09 cnf(d1, plain, ~'ilf$utype'(X0,'subset$utype'('cross$uproduct'(X1,X2))) | 'ilf$utype'(X0,'relation$utype'(X1,X2)) | ~'ilf$utype'(X2,'set$utype'), inference(resolution, [status(thm)], [c63,c5])).
% 28.18/7.09 cnf(d2, plain, ~'ilf$utype'(X0,'set$utype') | 'ilf$utype'(X0,'subset$utype'(X1)) | ~'ilf$utype'(X0,'member$utype'('power$uset'(X1))), inference(resolution, [status(thm)], [c63,c25])).
% 28.18/7.09 cnf(d3, plain, ~'ilf$utype'(X0,'set$utype') | 'ilf$utype'(X0,'member$utype'(X1)) | ~member(X0,X1) | empty(X1), inference(resolution, [status(thm)], [c63,c48])).
% 28.18/7.09 cnf(d4, plain, ~'ilf$utype'(X0,'set$utype') | ~member(X0,'power$uset'(X1)) | empty('power$uset'(X1)) | ~'ilf$utype'(X0,'set$utype') | 'ilf$utype'(X0,'subset$utype'(X1)), inference(resolution, [status(thm)], [d3,d2])).
% 28.18/7.09 cnf(d5, plain, 'ilf$utype'(X0,'subset$utype'(X1)) | ~member(X0,'power$uset'(X1)) | empty('power$uset'(X1)), inference(resolution, [status(thm)], [c63,d4])).
% 28.18/7.09 cnf(d6, plain, ~empty('power$uset'(X0)), inference(resolution, [status(thm)], [c63,c45])).
% 28.18/7.09 cnf(d7, plain, 'ilf$utype'(X0,'subset$utype'(X1)) | ~member(X0,'power$uset'(X1)), inference(resolution, [status(thm)], [d6,d5])).
% 28.18/7.09 cnf(d8, plain, ~'ilf$utype'(X0,'set$utype') | member(X1,'power$uset'(X0)) | ~member(sK50(X1,X0),X0), inference(resolution, [status(thm)], [c63,c44])).
% 28.18/7.09 cnf(d9, plain, ~'ilf$utype'(X0,'set$utype') | member(X1,'power$uset'(X0)) | member(sK50(X1,X0),X1), inference(resolution, [status(thm)], [c63,c43])).
% 28.18/7.09 cnf(d10, plain, X0 = X1 | ~member(X0,X2) | ~'Ts13'(X1,X2), inference(resolution, [status(thm)], [c63,c10])).
% 28.18/7.09 cnf(d11, plain, X0 != singleton(X1) | ~'ilf$utype'(X1,'set$utype') | ~'ilf$utype'(X0,'set$utype') | 'Ts13'(X1,X0), inference(resolution, [status(thm)], [c63,c8])).
% 28.18/7.09 cnf(d12, plain, ~'ilf$utype'(X0,'set$utype') | ~'ilf$utype'(singleton(X0),'set$utype') | 'Ts13'(X0,singleton(X0)), inference(equality_resolution, [status(thm)], [d11])).
% 28.18/7.09 cnf(d13, plain, ~'ilf$utype'(singleton(X0),'set$utype') | 'Ts13'(X0,singleton(X0)), inference(resolution, [status(thm)], [c63,d12])).
% 28.18/7.09 cnf(d14, plain, 'Ts13'(X0,singleton(X0)), inference(resolution, [status(thm)], [d13,c63])).
% 28.18/7.09 cnf(d15, plain, X0 = X1 | ~member(X0,singleton(X1)), inference(resolution, [status(thm)], [d14,d10])).
% 28.18/7.09 cnf(d16, plain, sK50(singleton(X0),X1) = X0 | ~'ilf$utype'(X1,'set$utype') | member(singleton(X0),'power$uset'(X1)), inference(resolution, [status(thm)], [d15,d9])).
% 28.18/7.09 cnf(d17, plain, sK50(singleton(X0),X1) = X0 | member(singleton(X0),'power$uset'(X1)), inference(resolution, [status(thm)], [c63,d16])).
% 28.18/7.09 cnf(d18, plain, ~member(X0,X1) | ~'ilf$utype'(X1,'set$utype') | member(singleton(X0),'power$uset'(X1)) | member(singleton(X0),'power$uset'(X1)), inference(superposition, [status(thm)], [d17,d8])).
% 28.18/7.09 cnf(d19, plain, ~member(X0,X1) | member(singleton(X0),'power$uset'(X1)), inference(resolution, [status(thm)], [c63,d18])).
% 28.18/7.09 cnf(d20, plain, ~member(X0,X1) | 'ilf$utype'(singleton(X0),'subset$utype'(X1)), inference(resolution, [status(thm)], [d19,d7])).
% 28.18/7.09 cnf(d21, plain, ~member(X0,'cross$uproduct'(X1,X2)) | ~'ilf$utype'(X2,'set$utype') | 'ilf$utype'(singleton(X0),'relation$utype'(X1,X2)), inference(resolution, [status(thm)], [d20,d1])).
% 28.18/7.09 cnf(d22, plain, 'ilf$utype'(singleton(X0),'relation$utype'(X1,X2)) | ~member(X0,'cross$uproduct'(X1,X2)), inference(resolution, [status(thm)], [c63,d21])).
% 28.18/7.09 cnf(d23, plain, ~member('ordered$upair'(sK74,sK75),'cross$uproduct'(sK72,sK73)), inference(resolution, [status(thm)], [d22,c70])).
% 28.18/7.09 cnf(d24, plain, ~'ilf$utype'(sK75,'set$utype') | ~'ilf$utype'(sK72,'set$utype') | ~'ilf$utype'(sK74,'set$utype') | ~member(sK75,sK73) | ~member(sK74,sK72), inference(resolution, [status(thm)], [d23,d0])).
% 28.18/7.09 cnf(d25, plain, ~'ilf$utype'(sK72,'set$utype') | ~'ilf$utype'(sK74,'set$utype') | ~'ilf$utype'(sK75,'set$utype') | ~member(sK75,sK73), inference(resolution, [status(thm)], [c68,d24])).
% 28.18/7.09 cnf(d26, plain, ~'ilf$utype'(sK72,'set$utype') | ~'ilf$utype'(sK74,'set$utype') | ~'ilf$utype'(sK75,'set$utype'), inference(resolution, [status(thm)], [c69,d25])).
% 28.18/7.09 cnf(d27, plain, ~'ilf$utype'(sK74,'set$utype') | ~'ilf$utype'(sK75,'set$utype'), inference(resolution, [status(thm)], [c63,d26])).
% 28.18/7.09 cnf(d28, plain, ~'ilf$utype'(sK74,'set$utype'), inference(resolution, [status(thm)], [d27,c63])).
% 28.18/7.09 cnf(d29, plain, $false, inference(resolution, [status(thm)], [c63,d28])).
% 28.18/7.09 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------