%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 08:41:18 AM UTC 2026
% Result : Theorem 93.52s 21.48s
% Output : CNFRefutation 93.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:52:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 93.52/21.48 % SZS status Theorem for theBenchmark.p
% 93.52/21.48 % SZS output start CNFRefutation for theBenchmark.p
% 93.52/21.48 fof(d10_relat_1, axiom, ! [X0] : ! [X1] : ((relation(X1) => (X1 = 'identity$urelation'(X0) <=> ! [X2] : ! [X3] : ((in('ordered$upair'(X2,X3),X1) <=> (in(X2,X0) & X2 = X3))))))).
% 93.52/21.48 fof(d4_funct_1, axiom, ! [X0] : (((relation(X0) & function(X0)) => ! [X1] : ! [X2] : (((in(X1,'relation$udom'(X0)) => (X2 = apply(X0,X1) <=> in('ordered$upair'(X1,X2),X0))) & (~in(X1,'relation$udom'(X0)) => (X2 = apply(X0,X1) <=> X2 = 'empty$uset'))))))).
% 93.52/21.48 fof(dt_k6_relat_1, axiom, ! [X0] : relation('identity$urelation'(X0))).
% 93.52/21.48 fof(fc2_funct_1, axiom, ! [X0] : ((relation('identity$urelation'(X0)) & function('identity$urelation'(X0))))).
% 93.52/21.48 fof(t71_relat_1, axiom, ! [X0] : (('relation$udom'('identity$urelation'(X0)) = X0 & 'relation$urng'('identity$urelation'(X0)) = X0))).
% 93.52/21.48 fof(t8_funct_1, axiom, ! [X0] : ! [X1] : ! [X2] : (((relation(X2) & function(X2)) => (in('ordered$upair'(X0,X1),X2) <=> (in(X0,'relation$udom'(X2)) & X1 = apply(X2,X0)))))).
% 93.52/21.48 fof(t34_funct_1, conjecture, ! [X0] : ! [X1] : (((relation(X1) & function(X1)) => (X1 = 'identity$urelation'(X0) <=> ('relation$udom'(X1) = X0 & ! [X2] : ((in(X2,X0) => apply(X1,X2) = X2))))))).
% 93.52/21.48 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : (((relation(X1) & function(X1)) => (X1 = 'identity$urelation'(X0) <=> ('relation$udom'(X1) = X0 & ! [X2] : ((in(X2,X0) => apply(X1,X2) = X2)))))), inference(negate_conjecture, [status(cth)], [t34_funct_1])).
% 93.52/21.48 cnf(c4, plain, ~relation(X0) | X1(X2,X0), inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c5, plain, ~X0(X1,X2,X3,X4) | ~in('ordered$upair'(X3,X4),X2), inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c6, plain, ~X0(X1,X2,X3,X4) | X4 = X3, inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c7, plain, ~X0(X1,X2,X3,X4) | in(X3,X1), inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c9, plain, ~X0(X1,X2) | 'identity$urelation'(X1) != X2 | ~in('ordered$upair'(X3,X4),X2) | X4 = X3, inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c11, plain, ~X0(X1,X2) | 'identity$urelation'(X1) = X2 | in('ordered$upair'(sK12(X1,X2),sK13(X1,X2)),X2) | X3(X1,X2,sK12(X1,X2),sK13(X1,X2)), inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c12, plain, ~X0(X1,X2) | ~in(sK12(X1,X2),X1) | sK13(X1,X2) != sK12(X1,X2) | X3(X1,X2,sK12(X1,X2),sK13(X1,X2)) | 'identity$urelation'(X1) = X2, inference(clausification, [status(esa)], [d10_relat_1])).
% 93.52/21.48 cnf(c13, plain, in('ordered$upair'(X0,X1),X2) | ~function(X2) | ~in(X0,'relation$udom'(X2)) | ~relation(X2) | apply(X2,X0) != X1, inference(clausification, [status(esa)], [d4_funct_1])).
% 93.52/21.48 cnf(c18, plain, relation('identity$urelation'(X0)), inference(clausification, [status(esa)], [dt_k6_relat_1])).
% 93.52/21.48 cnf(c26, plain, function('identity$urelation'(X0)), inference(clausification, [status(esa)], [fc2_funct_1])).
% 93.52/21.48 cnf(c50, plain, 'relation$udom'('identity$urelation'(X0)) = X0, inference(clausification, [status(esa)], [t71_relat_1])).
% 93.52/21.48 cnf(c54, plain, ~function(X0) | ~relation(X0) | ~in('ordered$upair'(X1,X2),X0) | in(X1,'relation$udom'(X0)), inference(clausification, [status(esa)], [t8_funct_1])).
% 93.52/21.48 cnf(c55, plain, ~function(X0) | ~relation(X0) | ~in('ordered$upair'(X1,X2),X0) | apply(X0,X1) = X2, inference(clausification, [status(esa)], [t8_funct_1])).
% 93.52/21.48 cnf(c57, plain, function(sK53), inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c58, plain, relation(sK53), inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c59, plain, X0(sK52,sK53) | 'identity$urelation'(sK52) != sK53, inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c60, plain, X0(sK52,sK53) | ~in(X1,sK52) | apply(sK53,X1) = X1, inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c61, plain, X0(sK52,sK53) | 'relation$udom'(sK53) = sK52, inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c62, plain, ~X0(X1,X2) | 'identity$urelation'(X1) = X2, inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c63, plain, ~X0(X1,X2) | 'relation$udom'(X2) != X1 | in(sK55(X1,X2),X1), inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(c64, plain, ~X0(X1,X2) | 'relation$udom'(X2) != X1 | apply(X2,sK55(X1,X2)) != sK55(X1,X2), inference(clausification, [status(esa)], [negated_conjecture])).
% 93.52/21.48 cnf(d0, plain, 'identity$urelation'(X0) = X1 | in('ordered$upair'(sK12(X0,X1),sK13(X0,X1)),X1) | ~'Ts7'(X0,X1) | in(sK12(X0,X1),X0), inference(resolution, [status(thm)], [c11,c7])).
% 93.52/21.48 cnf(d1, plain, 'identity$urelation'(X0) = X1 | in(sK12(X0,X1),X0) | ~'Ts7'(X0,X1) | in(sK12(X0,X1),'relation$udom'(X1)) | ~function(X1) | ~relation(X1), inference(resolution, [status(thm)], [d0,c54])).
% 93.52/21.48 cnf(d2, plain, 'identity$urelation'(sK52) = sK53 | 'relation$udom'(sK53) = sK52, inference(resolution, [status(thm)], [c62,c61])).
% 93.52/21.48 cnf(d3, plain, in(sK12(X0,sK53),sK52) | 'identity$urelation'(X0) = sK53 | in(sK12(X0,sK53),X0) | ~function(sK53) | ~relation(sK53) | ~'Ts7'(X0,sK53) | 'identity$urelation'(sK52) = sK53, inference(superposition, [status(thm)], [d2,d1])).
% 93.52/21.48 cnf(d4, plain, 'identity$urelation'(X0) = sK53 | 'identity$urelation'(sK52) = sK53 | in(sK12(X0,sK53),X0) | in(sK12(X0,sK53),sK52) | ~relation(sK53) | ~'Ts7'(X0,sK53), inference(resolution, [status(thm)], [c57,d3])).
% 93.52/21.48 cnf(d5, plain, 'identity$urelation'(X0) = sK53 | 'identity$urelation'(sK52) = sK53 | in(sK12(X0,sK53),X0) | in(sK12(X0,sK53),sK52) | ~'Ts7'(X0,sK53), inference(resolution, [status(thm)], [c58,d4])).
% 93.52/21.48 cnf(d6, plain, 'identity$urelation'(sK52) = sK53 | 'identity$urelation'(sK52) = sK53 | in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53), inference(factoring, [status(thm)], [d5])).
% 93.52/21.48 cnf(d7, plain, ~in(X0,'relation$udom'(X1)) | in('ordered$upair'(X0,apply(X1,X0)),X1) | ~function(X1) | ~relation(X1), inference(equality_resolution, [status(thm)], [c13])).
% 93.52/21.48 cnf(d8, plain, 'identity$urelation'(sK52) = sK53 | ~'Ts7'(sK52,sK53) | apply(sK53,sK12(sK52,sK53)) = sK12(sK52,sK53) | 'Ts51'(sK52,sK53), inference(resolution, [status(thm)], [d6,c60])).
% 93.52/21.48 cnf(d9, plain, 'identity$urelation'(sK52) = sK53 | apply(sK53,sK12(sK52,sK53)) = sK12(sK52,sK53) | 'Ts51'(sK52,sK53) | ~relation(sK53), inference(resolution, [status(thm)], [d8,c4])).
% 93.52/21.48 cnf(d10, plain, 'identity$urelation'(sK52) = sK53 | apply(sK53,sK12(sK52,sK53)) = sK12(sK52,sK53) | 'Ts51'(sK52,sK53), inference(resolution, [status(thm)], [c58,d9])).
% 93.52/21.48 cnf(d11, plain, 'identity$urelation'(sK52) = sK53 | apply(sK53,sK12(sK52,sK53)) = sK12(sK52,sK53) | 'identity$urelation'(sK52) = sK53, inference(resolution, [status(thm)], [d10,c62])).
% 93.52/21.48 cnf(d12, plain, in('ordered$upair'(sK12(sK52,sK53),sK12(sK52,sK53)),sK53) | ~in(sK12(sK52,sK53),'relation$udom'(sK53)) | ~function(sK53) | ~relation(sK53) | 'identity$urelation'(sK52) = sK53, inference(superposition, [status(thm)], [d11,d7])).
% 93.52/21.48 cnf(d13, plain, 'identity$urelation'(sK52) = sK53 | in('ordered$upair'(sK12(sK52,sK53),sK12(sK52,sK53)),sK53) | ~in(sK12(sK52,sK53),'relation$udom'(sK53)) | ~relation(sK53), inference(resolution, [status(thm)], [c57,d12])).
% 93.52/21.48 cnf(d14, plain, 'identity$urelation'(sK52) = sK53 | in('ordered$upair'(sK12(sK52,sK53),sK12(sK52,sK53)),sK53) | ~in(sK12(sK52,sK53),'relation$udom'(sK53)), inference(resolution, [status(thm)], [c58,d13])).
% 93.52/21.48 cnf(d15, plain, 'identity$urelation'(X0) = X1 | in('ordered$upair'(sK12(X0,X1),sK13(X0,X1)),X1) | ~'Ts7'(X0,X1) | sK13(X0,X1) = sK12(X0,X1), inference(resolution, [status(thm)], [c11,c6])).
% 93.52/21.48 cnf(d16, plain, 'identity$urelation'(X0) = X1 | sK13(X0,X1) = sK12(X0,X1) | ~'Ts7'(X0,X1) | apply(X1,sK12(X0,X1)) = sK13(X0,X1) | ~function(X1) | ~relation(X1), inference(resolution, [status(thm)], [d15,c55])).
% 93.52/21.48 cnf(d17, plain, 'identity$urelation'(X0) = X1 | sK13(X0,X1) = sK12(X0,X1) | apply(X1,sK12(X0,X1)) = sK13(X0,X1) | ~function(X1) | ~relation(X1) | ~relation(X1), inference(resolution, [status(thm)], [d16,c4])).
% 93.52/21.48 cnf(d18, plain, 'identity$urelation'(X0) = sK53 | sK13(X0,sK53) = sK12(X0,sK53) | apply(sK53,sK12(X0,sK53)) = sK13(X0,sK53) | ~function(sK53), inference(resolution, [status(thm)], [d17,c58])).
% 93.52/21.48 cnf(d19, plain, 'identity$urelation'(X0) = sK53 | sK13(X0,sK53) = sK12(X0,sK53) | apply(sK53,sK12(X0,sK53)) = sK13(X0,sK53), inference(resolution, [status(thm)], [c57,d18])).
% 93.52/21.48 cnf(d20, plain, sK13(sK52,sK53) = sK12(sK52,sK53) | 'identity$urelation'(sK52) = sK53 | 'identity$urelation'(sK52) = sK53 | sK13(sK52,sK53) = sK12(sK52,sK53), inference(superposition, [status(thm)], [d19,d11])).
% 93.52/21.48 cnf(d21, plain, sK12(sK52,sK53) != sK12(sK52,sK53) | 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | 'Ts6'(sK52,sK53,sK12(sK52,sK53),sK13(sK52,sK53)) | 'identity$urelation'(sK52) = sK53, inference(superposition, [status(thm)], [d20,c12])).
% 93.52/21.48 cnf(d22, plain, 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | 'Ts6'(sK52,sK53,sK12(sK52,sK53),sK13(sK52,sK53)), inference(equality_resolution, [status(thm)], [d21])).
% 93.52/21.48 cnf(d23, plain, 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | ~in('ordered$upair'(sK12(sK52,sK53),sK13(sK52,sK53)),sK53), inference(resolution, [status(thm)], [d22,c5])).
% 93.52/21.48 cnf(d24, plain, ~in('ordered$upair'(sK12(sK52,sK53),sK12(sK52,sK53)),sK53) | 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | 'identity$urelation'(sK52) = sK53, inference(superposition, [status(thm)], [d20,d23])).
% 93.52/21.48 cnf(d25, plain, 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),'relation$udom'(sK53)), inference(resolution, [status(thm)], [d24,d14])).
% 93.52/21.48 cnf(d26, plain, ~in(sK12(sK52,sK53),sK52) | 'identity$urelation'(sK52) = sK53 | ~in(sK12(sK52,sK53),sK52) | ~'Ts7'(sK52,sK53) | 'identity$urelation'(sK52) = sK53, inference(superposition, [status(thm)], [d2,d25])).
% 93.52/21.48 cnf(d27, plain, 'identity$urelation'(sK52) = sK53 | ~'Ts7'(sK52,sK53) | 'identity$urelation'(sK52) = sK53 | ~'Ts7'(sK52,sK53), inference(resolution, [status(thm)], [d26,d6])).
% 93.52/21.48 cnf(d28, plain, 'identity$urelation'(sK52) = sK53 | ~relation(sK53), inference(resolution, [status(thm)], [d27,c4])).
% 93.52/21.48 cnf(d29, plain, 'identity$urelation'(sK52) = sK53, inference(resolution, [status(thm)], [c58,d28])).
% 93.52/21.48 cnf(d30, plain, 'relation$udom'(sK53) = sK52, inference(superposition, [status(thm)], [d29,c50])).
% 93.52/21.48 cnf(d31, plain, X0 = X1 | ~in('ordered$upair'(X1,X0),'identity$urelation'(X2)) | ~'Ts7'(X2,'identity$urelation'(X2)), inference(equality_resolution, [status(thm)], [c9])).
% 93.52/21.48 cnf(d32, plain, ~in(X0,'relation$udom'('identity$urelation'(X1))) | ~function('identity$urelation'(X1)) | ~relation('identity$urelation'(X1)) | apply('identity$urelation'(X1),X0) = X0 | ~'Ts7'(X1,'identity$urelation'(X1)), inference(resolution, [status(thm)], [d7,d31])).
% 93.52/21.48 cnf(d33, plain, apply('identity$urelation'(X0),X1) = X1 | ~in(X1,X0) | ~function('identity$urelation'(X0)) | ~relation('identity$urelation'(X0)) | ~'Ts7'(X0,'identity$urelation'(X0)), inference(demodulation, [status(thm)], [d32,c50])).
% 93.52/21.48 cnf(d34, plain, apply('identity$urelation'(X0),X1) = X1 | ~in(X1,X0) | ~function('identity$urelation'(X0)) | ~'Ts7'(X0,'identity$urelation'(X0)), inference(resolution, [status(thm)], [c18,d33])).
% 93.52/21.48 cnf(d35, plain, apply('identity$urelation'(X0),X1) = X1 | ~in(X1,X0) | ~'Ts7'(X0,'identity$urelation'(X0)), inference(resolution, [status(thm)], [c26,d34])).
% 93.52/21.48 cnf(d36, plain, apply('identity$urelation'(X0),X1) = X1 | ~in(X1,X0) | ~relation('identity$urelation'(X0)), inference(resolution, [status(thm)], [d35,c4])).
% 93.52/21.48 cnf(d37, plain, apply('identity$urelation'(X0),X1) = X1 | ~in(X1,X0), inference(resolution, [status(thm)], [c18,d36])).
% 93.52/21.48 cnf(d38, plain, X0 != X1 | in(sK55(X1,'identity$urelation'(X0)),X1) | ~'Ts51'(X1,'identity$urelation'(X0)), inference(superposition, [status(thm)], [c50,c63])).
% 93.52/21.48 cnf(d39, plain, in(sK55(X0,'identity$urelation'(X0)),X0) | ~'Ts51'(X0,'identity$urelation'(X0)), inference(equality_resolution, [status(thm)], [d38])).
% 93.52/21.48 cnf(d40, plain, in(sK55(sK52,sK53),sK52) | ~'Ts51'(sK52,'identity$urelation'(sK52)), inference(superposition, [status(thm)], [d29,d39])).
% 93.52/21.48 cnf(d41, plain, in(sK55(sK52,sK53),sK52) | ~'Ts51'(sK52,sK53), inference(demodulation, [status(thm)], [d40,d29])).
% 93.52/21.48 cnf(d42, plain, 'Ts51'(sK52,sK53), inference(resolution, [status(thm)], [d29,c59])).
% 93.52/21.48 cnf(d43, plain, in(sK55(sK52,sK53),sK52), inference(resolution, [status(thm)], [d42,d41])).
% 93.52/21.48 cnf(d44, plain, apply('identity$urelation'(sK52),sK55(sK52,sK53)) = sK55(sK52,sK53), inference(resolution, [status(thm)], [d43,d37])).
% 93.52/21.48 cnf(d45, plain, apply(sK53,sK55(sK52,sK53)) = sK55(sK52,sK53), inference(demodulation, [status(thm)], [d44,d29])).
% 93.52/21.48 cnf(d46, plain, sK55(sK52,sK53) != sK55(sK52,sK53) | 'relation$udom'(sK53) != sK52 | ~'Ts51'(sK52,sK53), inference(superposition, [status(thm)], [d45,c64])).
% 93.52/21.48 cnf(d47, plain, sK52 != sK52 | sK55(sK52,sK53) != sK55(sK52,sK53) | ~'Ts51'(sK52,sK53), inference(demodulation, [status(thm)], [d46,d30])).
% 93.52/21.48 cnf(d48, plain, sK52 != sK52 | sK55(sK52,sK53) != sK55(sK52,sK53), inference(resolution, [status(thm)], [d42,d47])).
% 93.52/21.48 cnf(d49, plain, sK52 != sK52, inference(equality_resolution, [status(thm)], [d48])).
% 93.52/21.48 cnf(d50, plain, $false, inference(equality_resolution, [status(thm)], [d49])).
% 93.52/21.48 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------