%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:40:50 AM UTC 2026
% Result : Theorem 14.97s 2.94s
% Output : CNFRefutation 14.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:36:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.97/2.94 % SZS status Theorem for theBenchmark.p
% 14.97/2.94 % SZS output start CNFRefutation for theBenchmark.p
% 14.97/2.94 fof(d5_funct_1, axiom, ! [X0] : (((relation(X0) & function(X0)) => ! [X1] : ((X1 = 'relation$urng'(X0) <=> ! [X2] : ((in(X2,X1) <=> ? [X3] : ((in(X3,'relation$udom'(X0)) & X2 = apply(X0,X3)))))))))).
% 14.97/2.94 fof(d8_funct_1, axiom, ! [X0] : (((relation(X0) & function(X0)) => ('one$uto$uone'(X0) <=> ! [X1] : ! [X2] : (((in(X1,'relation$udom'(X0)) & (in(X2,'relation$udom'(X0)) & apply(X0,X1) = apply(X0,X2))) => X1 = X2)))))).
% 14.97/2.94 fof(t117_funct_1, axiom, ! [X0] : ! [X1] : (((relation(X1) & function(X1)) => (in(X0,'relation$udom'(X1)) => 'relation$uimage'(X1,singleton(X0)) = singleton(apply(X1,X0)))))).
% 14.97/2.94 fof(t142_funct_1, axiom, ! [X0] : ! [X1] : ((relation(X1) => (in(X0,'relation$urng'(X1)) <=> 'relation$uinverse$uimage'(X1,singleton(X0)) != 'empty$uset')))).
% 14.97/2.94 fof(t39_zfmisc_1, axiom, ! [X0] : ! [X1] : ((subset(X0,singleton(X1)) <=> (X0 = 'empty$uset' | X0 = singleton(X1))))).
% 14.97/2.94 fof(t6_zfmisc_1, axiom, ! [X0] : ! [X1] : ((subset(singleton(X0),singleton(X1)) => X0 = X1))).
% 14.97/2.94 fof(t153_funct_1, conjecture, ! [X0] : (((relation(X0) & function(X0)) => (! [X1] : subset('relation$uinverse$uimage'(X0,'relation$uimage'(X0,X1)),X1) => 'one$uto$uone'(X0))))).
% 14.97/2.94 fof(negated_conjecture, negated_conjecture, ~! [X0] : (((relation(X0) & function(X0)) => (! [X1] : subset('relation$uinverse$uimage'(X0,'relation$uimage'(X0,X1)),X1) => 'one$uto$uone'(X0)))), inference(negate_conjecture, [status(cth)], [t153_funct_1])).
% 14.97/2.94 cnf(c6, plain, ~relation(X0) | ~function(X0) | X1 != 'relation$urng'(X0) | X2(X0,X1), inference(clausification, [status(esa)], [d5_funct_1])).
% 14.97/2.94 cnf(c10, plain, ~X0(X1,X2) | in(X3,X2) | ~in(X4,'relation$udom'(X1)) | X3 != apply(X1,X4), inference(clausification, [status(esa)], [d5_funct_1])).
% 14.97/2.94 cnf(c18, plain, ~relation(X0) | ~function(X0) | 'one$uto$uone'(X0) | ~X1(X0), inference(clausification, [status(esa)], [d8_funct_1])).
% 14.97/2.94 cnf(c20, plain, X0(X1) | in(sK18(X1),'relation$udom'(X1)), inference(clausification, [status(esa)], [d8_funct_1])).
% 14.97/2.94 cnf(c21, plain, X0(X1) | in(sK19(X1),'relation$udom'(X1)), inference(clausification, [status(esa)], [d8_funct_1])).
% 14.97/2.94 cnf(c22, plain, X0(X1) | apply(X1,sK18(X1)) = apply(X1,sK19(X1)), inference(clausification, [status(esa)], [d8_funct_1])).
% 14.97/2.94 cnf(c23, plain, X0(X1) | sK18(X1) != sK19(X1), inference(clausification, [status(esa)], [d8_funct_1])).
% 14.97/2.94 cnf(c60, plain, ~relation(X0) | ~function(X0) | ~in(X1,'relation$udom'(X0)) | 'relation$uimage'(X0,singleton(X1)) = singleton(apply(X0,X1)), inference(clausification, [status(esa)], [t117_funct_1])).
% 14.97/2.94 cnf(c61, plain, ~relation(X0) | ~in(X1,'relation$urng'(X0)) | 'relation$uinverse$uimage'(X0,singleton(X1)) != 'empty$uset', inference(clausification, [status(esa)], [t142_funct_1])).
% 14.97/2.94 cnf(c65, plain, ~subset(X0,singleton(X1)) | X0 = 'empty$uset' | X0 = singleton(X1), inference(clausification, [status(esa)], [t39_zfmisc_1])).
% 14.97/2.94 cnf(c73, plain, ~subset(singleton(X0),singleton(X1)) | X0 = X1, inference(clausification, [status(esa)], [t6_zfmisc_1])).
% 14.97/2.94 cnf(c76, plain, relation(sK67), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.97/2.94 cnf(c77, plain, function(sK67), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.97/2.94 cnf(c78, plain, subset('relation$uinverse$uimage'(sK67,'relation$uimage'(sK67,X0)),X0), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.97/2.94 cnf(c79, plain, ~'one$uto$uone'(sK67), inference(clausification, [status(esa)], [negated_conjecture])).
% 14.97/2.94 cnf(d0, plain, ~function(X0) | ~relation(X0) | 'Ts5'(X0,'relation$urng'(X0)), inference(equality_resolution, [status(thm)], [c6])).
% 14.97/2.94 cnf(d1, plain, ~in(X0,'relation$udom'(X1)) | in(apply(X1,X0),X2) | ~'Ts5'(X1,X2), inference(equality_resolution, [status(thm)], [c10])).
% 14.97/2.94 cnf(d2, plain, apply(X0,sK18(X0)) = apply(X0,sK19(X0)) | ~function(X0) | ~relation(X0) | 'one$uto$uone'(X0), inference(resolution, [status(thm)], [c22,c18])).
% 14.97/2.94 cnf(d3, plain, apply(sK67,sK18(sK67)) = apply(sK67,sK19(sK67)) | ~function(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [d2,c76])).
% 14.97/2.94 cnf(d4, plain, apply(sK67,sK18(sK67)) = apply(sK67,sK19(sK67)) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c77,d3])).
% 14.97/2.94 cnf(d5, plain, apply(sK67,sK18(sK67)) = apply(sK67,sK19(sK67)), inference(resolution, [status(thm)], [c79,d4])).
% 14.97/2.94 cnf(d6, plain, in(apply(sK67,sK18(sK67)),X0) | ~in(sK19(sK67),'relation$udom'(sK67)) | ~'Ts5'(sK67,X0), inference(superposition, [status(thm)], [d5,d1])).
% 14.97/2.94 cnf(d7, plain, 'relation$uimage'(X0,singleton(sK18(X0))) = singleton(apply(X0,sK18(X0))) | ~function(X0) | ~relation(X0) | 'Ts14'(X0), inference(resolution, [status(thm)], [c60,c20])).
% 14.97/2.94 cnf(d8, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | 'Ts14'(sK67), inference(resolution, [status(thm)], [d7,c76])).
% 14.97/2.94 cnf(d9, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))) | 'Ts14'(sK67), inference(resolution, [status(thm)], [c77,d8])).
% 14.97/2.94 cnf(d10, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | ~relation(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [d9,c18])).
% 14.97/2.94 cnf(d11, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c76,d10])).
% 14.97/2.94 cnf(d12, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c77,d11])).
% 14.97/2.94 cnf(d13, plain, 'relation$uimage'(sK67,singleton(sK18(sK67))) = singleton(apply(sK67,sK18(sK67))), inference(resolution, [status(thm)], [c79,d12])).
% 14.97/2.94 cnf(d14, plain, subset('relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))),singleton(sK18(sK67))), inference(superposition, [status(thm)], [d13,c78])).
% 14.97/2.94 cnf(d15, plain, 'relation$uimage'(X0,singleton(sK19(X0))) = singleton(apply(X0,sK19(X0))) | ~function(X0) | ~relation(X0) | 'Ts14'(X0), inference(resolution, [status(thm)], [c60,c21])).
% 14.97/2.94 cnf(d16, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK19(sK67))) | ~function(sK67) | 'Ts14'(sK67), inference(resolution, [status(thm)], [d15,c76])).
% 14.97/2.94 cnf(d17, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | 'Ts14'(sK67), inference(demodulation, [status(thm)], [d16,d5])).
% 14.97/2.94 cnf(d18, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))) | 'Ts14'(sK67), inference(resolution, [status(thm)], [c77,d17])).
% 14.97/2.94 cnf(d19, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | ~relation(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [d18,c18])).
% 14.97/2.94 cnf(d20, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))) | ~function(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c76,d19])).
% 14.97/2.94 cnf(d21, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c77,d20])).
% 14.97/2.94 cnf(d22, plain, 'relation$uimage'(sK67,singleton(sK19(sK67))) = singleton(apply(sK67,sK18(sK67))), inference(resolution, [status(thm)], [c79,d21])).
% 14.97/2.94 cnf(d23, plain, 'relation$uinverse$uimage'(sK67,'relation$uimage'(sK67,singleton(X0))) = 'empty$uset' | 'relation$uinverse$uimage'(sK67,'relation$uimage'(sK67,singleton(X0))) = singleton(X0), inference(resolution, [status(thm)], [c65,c78])).
% 14.97/2.94 cnf(d24, plain, 'relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))) = singleton(sK19(sK67)) | 'relation$uinverse$uimage'(sK67,'relation$uimage'(sK67,singleton(sK19(sK67)))) = 'empty$uset', inference(superposition, [status(thm)], [d22,d23])).
% 14.97/2.94 cnf(d25, plain, 'relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))) = singleton(sK19(sK67)) | 'relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))) = 'empty$uset', inference(demodulation, [status(thm)], [d24,d22])).
% 14.97/2.94 cnf(d26, plain, subset(singleton(sK19(sK67)),singleton(sK18(sK67))) | 'relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))) = 'empty$uset', inference(superposition, [status(thm)], [d25,d14])).
% 14.97/2.94 cnf(d27, plain, 'relation$uinverse$uimage'(sK67,singleton(apply(sK67,sK18(sK67)))) = 'empty$uset' | sK19(sK67) = sK18(sK67), inference(resolution, [status(thm)], [d26,c73])).
% 14.97/2.94 cnf(d28, plain, 'empty$uset' != 'empty$uset' | ~in(apply(sK67,sK18(sK67)),'relation$urng'(sK67)) | ~relation(sK67) | sK19(sK67) = sK18(sK67), inference(superposition, [status(thm)], [d27,c61])).
% 14.97/2.94 cnf(d29, plain, sK19(sK67) = sK18(sK67) | 'empty$uset' != 'empty$uset' | ~in(apply(sK67,sK18(sK67)),'relation$urng'(sK67)), inference(resolution, [status(thm)], [c76,d28])).
% 14.97/2.94 cnf(d30, plain, sK19(sK67) = sK18(sK67) | ~in(apply(sK67,sK18(sK67)),'relation$urng'(sK67)), inference(equality_resolution, [status(thm)], [d29])).
% 14.97/2.94 cnf(d31, plain, sK19(sK67) = sK18(sK67) | ~in(sK19(sK67),'relation$udom'(sK67)) | ~'Ts5'(sK67,'relation$urng'(sK67)), inference(resolution, [status(thm)], [d30,d6])).
% 14.97/2.94 cnf(d32, plain, sK19(sK67) = sK18(sK67) | ~'Ts5'(sK67,'relation$urng'(sK67)) | 'Ts14'(sK67), inference(resolution, [status(thm)], [d31,c21])).
% 14.97/2.94 cnf(d33, plain, sK19(sK67) = sK18(sK67) | 'Ts14'(sK67) | ~function(sK67) | ~relation(sK67), inference(resolution, [status(thm)], [d32,d0])).
% 14.97/2.94 cnf(d34, plain, sK19(sK67) = sK18(sK67) | ~function(sK67) | 'Ts14'(sK67), inference(resolution, [status(thm)], [c76,d33])).
% 14.97/2.94 cnf(d35, plain, sK19(sK67) = sK18(sK67) | 'Ts14'(sK67), inference(resolution, [status(thm)], [c77,d34])).
% 14.97/2.94 cnf(d36, plain, sK19(sK67) = sK18(sK67) | ~function(sK67) | ~relation(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [d35,c18])).
% 14.97/2.94 cnf(d37, plain, sK19(sK67) = sK18(sK67) | ~function(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c76,d36])).
% 14.97/2.94 cnf(d38, plain, sK19(sK67) = sK18(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c77,d37])).
% 14.97/2.94 cnf(d39, plain, sK19(sK67) = sK18(sK67), inference(resolution, [status(thm)], [c79,d38])).
% 14.97/2.94 cnf(d40, plain, sK18(sK67) != sK18(sK67) | 'Ts14'(sK67), inference(superposition, [status(thm)], [d39,c23])).
% 14.97/2.94 cnf(d41, plain, 'Ts14'(sK67), inference(equality_resolution, [status(thm)], [d40])).
% 14.97/2.94 cnf(d42, plain, ~function(sK67) | ~relation(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [d41,c18])).
% 14.97/2.94 cnf(d43, plain, ~function(sK67) | 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c76,d42])).
% 14.97/2.94 cnf(d44, plain, 'one$uto$uone'(sK67), inference(resolution, [status(thm)], [c77,d43])).
% 14.97/2.94 cnf(d45, plain, $false, inference(resolution, [status(thm)], [c79,d44])).
% 14.97/2.94 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------