%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET995+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:33:42 AM UTC 2026
% Result : Theorem 41.30s 11.04s
% Output : CNFRefutation 41.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET995+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.56 % Computer : n004.cluster.edu
% 0.08/5.56 % Model : x86_64 x86_64
% 0.08/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.56 % Memory : 8046.5625MB
% 0.08/5.56 % OS : Linux 6.8.0-71-generic
% 0.08/5.56 % CPULimit : 300
% 0.08/5.56 % WCLimit : 300
% 0.08/5.56 % DateTime : Sat Sep 26 08:29:42 UTC 2026
% 0.08/5.56 % CPUTime :
% 0.08/5.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.30/11.04 % SZS status Theorem for theBenchmark.p
% 41.30/11.04 % SZS output start CNFRefutation for theBenchmark.p
% 41.30/11.04 fof(d1_tarski, axiom, ! [X0] : ! [X1] : ((X1 = singleton(X0) <=> ! [X2] : ((in(X2,X1) <=> X2 = X0))))).
% 41.30/11.04 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)))))))))).
% 41.30/11.04 fof(existence_m1_subset_1, axiom, ! [X0] : ? [X1] : element(X1,X0)).
% 41.30/11.04 fof(fc2_subset_1, axiom, ! [X0] : ~empty(singleton(X0))).
% 41.30/11.04 fof(fc5_relat_1, axiom, ! [X0] : (((~empty(X0) & relation(X0)) => ~empty('relation$udom'(X0))))).
% 41.30/11.04 fof(fc8_relat_1, axiom, ! [X0] : ((empty(X0) => (empty('relation$urng'(X0)) & relation('relation$urng'(X0)))))).
% 41.30/11.04 fof(t2_subset, axiom, ! [X0] : ! [X1] : ((element(X0,X1) => (empty(X1) | in(X0,X1))))).
% 41.30/11.04 fof(t9_funct_1, axiom, ! [X0] : (((relation(X0) & function(X0)) => ! [X1] : (((relation(X1) & function(X1)) => (('relation$udom'(X0) = 'relation$udom'(X1) & ! [X2] : ((in(X2,'relation$udom'(X0)) => apply(X0,X2) = apply(X1,X2)))) => X0 = X1)))))).
% 41.30/11.04 fof(t17_funct_1, conjecture, ! [X0] : ! [X1] : (((relation(X1) & function(X1)) => ! [X2] : (((relation(X2) & function(X2)) => (('relation$udom'(X1) = 'relation$udom'(X2) & ('relation$urng'(X1) = singleton(X0) & 'relation$urng'(X2) = singleton(X0))) => X1 = X2)))))).
% 41.30/11.04 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : (((relation(X1) & function(X1)) => ! [X2] : (((relation(X2) & function(X2)) => (('relation$udom'(X1) = 'relation$udom'(X2) & ('relation$urng'(X1) = singleton(X0) & 'relation$urng'(X2) = singleton(X0))) => X1 = X2))))), inference(negate_conjecture, [status(cth)], [t17_funct_1])).
% 41.30/11.04 cnf(c3, plain, singleton(X0) != X1 | ~in(X2,X1) | X0 = X2, inference(clausification, [status(esa)], [d1_tarski])).
% 41.30/11.04 cnf(c4, plain, singleton(X0) != X1 | in(X2,X1) | X0 != X2, inference(clausification, [status(esa)], [d1_tarski])).
% 41.30/11.04 cnf(c9, plain, ~function(X0) | ~relation(X0) | X1(X0), inference(clausification, [status(esa)], [d5_funct_1])).
% 41.30/11.04 cnf(c13, plain, ~X0(X1) | 'relation$urng'(X1) != X2 | ~in(X3,X2) | in(sK14(X1,X3),'relation$udom'(X1)), inference(clausification, [status(esa)], [d5_funct_1])).
% 41.30/11.04 cnf(c15, plain, 'relation$urng'(X0) != X1 | apply(X0,X2) != X3 | in(X3,X1) | ~in(X2,'relation$udom'(X0)) | ~X4(X0), inference(clausification, [status(esa)], [d5_funct_1])).
% 41.30/11.04 cnf(c18, plain, element(sK19(X0),X0), inference(clausification, [status(esa)], [existence_m1_subset_1])).
% 41.30/11.04 cnf(c24, plain, ~empty(singleton(X0)), inference(clausification, [status(esa)], [fc2_subset_1])).
% 41.30/11.04 cnf(c27, plain, ~relation(X0) | empty(X0) | ~empty('relation$udom'(X0)), inference(clausification, [status(esa)], [fc5_relat_1])).
% 41.30/11.04 cnf(c31, plain, ~empty(X0) | empty('relation$urng'(X0)), inference(clausification, [status(esa)], [fc8_relat_1])).
% 41.30/11.04 cnf(c49, plain, ~element(X0,X1) | in(X0,X1) | empty(X1), inference(clausification, [status(esa)], [t2_subset])).
% 41.30/11.04 cnf(c57, plain, ~function(X0) | in(sK57(X0,X1),'relation$udom'(X0)) | ~relation(X0) | ~relation(X1) | ~function(X1) | 'relation$udom'(X1) != 'relation$udom'(X0) | X1 = X0, inference(clausification, [status(esa)], [t9_funct_1])).
% 41.30/11.04 cnf(c58, plain, ~function(X0) | apply(X1,sK57(X0,X1)) != apply(X0,sK57(X0,X1)) | ~relation(X0) | ~relation(X1) | ~function(X1) | 'relation$udom'(X1) != 'relation$udom'(X0) | X1 = X0, inference(clausification, [status(esa)], [t9_funct_1])).
% 41.30/11.04 cnf(c59, plain, function(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c60, plain, relation(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c61, plain, function(sK60), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c62, plain, relation(sK60), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c63, plain, sK60 != sK59, inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c64, plain, 'relation$udom'(sK60) = 'relation$udom'(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c65, plain, singleton(sK58) = 'relation$urng'(sK60), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(c66, plain, singleton(sK58) = 'relation$urng'(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 41.30/11.04 cnf(d0, plain, 'relation$udom'(sK59) != 'relation$udom'(X0) | sK60 = X0 | in(sK57(X0,sK60),'relation$udom'(X0)) | ~function(X0) | ~function(sK60) | ~relation(X0) | ~relation(sK60), inference(superposition, [status(thm)], [c64,c57])).
% 41.30/11.04 cnf(d1, plain, 'relation$udom'(sK59) != 'relation$udom'(X0) | sK60 = X0 | in(sK57(X0,sK60),'relation$udom'(X0)) | ~function(X0) | ~relation(X0) | ~relation(sK60), inference(resolution, [status(thm)], [c61,d0])).
% 41.30/11.04 cnf(d2, plain, 'relation$udom'(sK59) != 'relation$udom'(X0) | sK60 = X0 | in(sK57(X0,sK60),'relation$udom'(X0)) | ~function(X0) | ~relation(X0), inference(resolution, [status(thm)], [c62,d1])).
% 41.30/11.04 cnf(d3, plain, sK60 = sK59 | in(sK57(sK59,sK60),'relation$udom'(sK59)) | ~function(sK59) | ~relation(sK59), inference(equality_resolution, [status(thm)], [d2])).
% 41.30/11.04 cnf(d4, plain, sK60 = sK59 | in(sK57(sK59,sK60),'relation$udom'(sK59)) | ~relation(sK59), inference(resolution, [status(thm)], [c59,d3])).
% 41.30/11.04 cnf(d5, plain, sK60 = sK59 | in(sK57(sK59,sK60),'relation$udom'(sK59)), inference(resolution, [status(thm)], [c60,d4])).
% 41.30/11.04 cnf(d6, plain, in(sK57(sK59,sK60),'relation$udom'(sK59)), inference(resolution, [status(thm)], [c63,d5])).
% 41.30/11.04 cnf(d7, plain, X0 = X1 | ~in(X1,singleton(X0)), inference(equality_resolution, [status(thm)], [c3])).
% 41.30/11.04 cnf(d8, plain, 'relation$urng'(X0) != X1 | in(apply(X0,X2),X1) | ~in(X2,'relation$udom'(X0)) | ~'Ts9'(X0), inference(equality_resolution, [status(thm)], [c15])).
% 41.30/11.04 cnf(d9, plain, singleton(sK58) != X0 | ~in(X1,'relation$udom'(sK59)) | in(apply(sK59,X1),X0) | ~'Ts9'(sK59), inference(superposition, [status(thm)], [c66,d8])).
% 41.30/11.04 cnf(d10, plain, ~function(sK59) | 'Ts9'(sK59), inference(resolution, [status(thm)], [c9,c60])).
% 41.30/11.04 cnf(d11, plain, 'Ts9'(sK59), inference(resolution, [status(thm)], [c59,d10])).
% 41.30/11.04 cnf(d12, plain, singleton(sK58) != X0 | ~in(X1,'relation$udom'(sK59)) | in(apply(sK59,X1),X0), inference(resolution, [status(thm)], [d11,d9])).
% 41.30/11.04 cnf(d13, plain, ~in(X0,'relation$udom'(sK59)) | in(apply(sK59,X0),singleton(sK58)), inference(equality_resolution, [status(thm)], [d12])).
% 41.30/11.04 cnf(d14, plain, ~in(X0,'relation$udom'(sK59)) | sK58 = apply(sK59,X0), inference(resolution, [status(thm)], [d13,d7])).
% 41.30/11.04 cnf(d15, plain, sK58 = apply(sK59,sK57(sK59,sK60)), inference(resolution, [status(thm)], [d14,d6])).
% 41.30/11.04 cnf(d16, plain, singleton(sK58) != X0 | ~in(X1,'relation$udom'(sK60)) | in(apply(sK60,X1),X0) | ~'Ts9'(sK60), inference(superposition, [status(thm)], [c65,d8])).
% 41.30/11.04 cnf(d17, plain, singleton(sK58) != X0 | ~in(X1,'relation$udom'(sK59)) | in(apply(sK60,X1),X0) | ~'Ts9'(sK60), inference(demodulation, [status(thm)], [d16,c64])).
% 41.30/11.04 cnf(d18, plain, ~function(sK60) | 'Ts9'(sK60), inference(resolution, [status(thm)], [c9,c62])).
% 41.30/11.04 cnf(d19, plain, 'Ts9'(sK60), inference(resolution, [status(thm)], [c61,d18])).
% 41.30/11.04 cnf(d20, plain, singleton(sK58) != X0 | ~in(X1,'relation$udom'(sK59)) | in(apply(sK60,X1),X0), inference(resolution, [status(thm)], [d19,d17])).
% 41.30/11.04 cnf(d21, plain, ~in(X0,'relation$udom'(sK59)) | in(apply(sK60,X0),singleton(sK58)), inference(equality_resolution, [status(thm)], [d20])).
% 41.30/11.04 cnf(d22, plain, ~in(X0,'relation$udom'(sK59)) | sK58 = apply(sK60,X0), inference(resolution, [status(thm)], [d21,d7])).
% 41.30/11.04 cnf(d23, plain, sK58 = apply(sK60,sK57(sK59,sK60)), inference(resolution, [status(thm)], [d22,d6])).
% 41.30/11.04 cnf(d24, plain, sK58 != apply(sK59,sK57(sK59,sK60)) | sK60 = sK59 | 'relation$udom'(sK60) != 'relation$udom'(sK59) | ~function(sK59) | ~function(sK60) | ~relation(sK59) | ~relation(sK60), inference(superposition, [status(thm)], [d23,c58])).
% 41.30/11.04 cnf(d25, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != apply(sK59,sK57(sK59,sK60)) | ~function(sK59) | ~function(sK60) | ~relation(sK59) | ~relation(sK60), inference(demodulation, [status(thm)], [d24,c64])).
% 41.30/11.04 cnf(d26, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != sK58 | ~function(sK59) | ~function(sK60) | ~relation(sK59) | ~relation(sK60), inference(demodulation, [status(thm)], [d25,d15])).
% 41.30/11.04 cnf(d27, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != sK58 | ~function(sK60) | ~relation(sK59) | ~relation(sK60), inference(resolution, [status(thm)], [c59,d26])).
% 41.30/11.04 cnf(d28, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != sK58 | ~function(sK60) | ~relation(sK60), inference(resolution, [status(thm)], [c60,d27])).
% 41.30/11.04 cnf(d29, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != sK58 | ~relation(sK60), inference(resolution, [status(thm)], [c61,d28])).
% 41.30/11.04 cnf(d30, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK60 = sK59 | sK58 != sK58, inference(resolution, [status(thm)], [c62,d29])).
% 41.30/11.04 cnf(d31, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59) | sK58 != sK58, inference(resolution, [status(thm)], [c63,d30])).
% 41.30/11.04 cnf(d32, plain, X0 != X1 | in(X1,singleton(X0)), inference(equality_resolution, [status(thm)], [c4])).
% 41.30/11.04 cnf(d33, plain, in(X0,singleton(X0)), inference(equality_resolution, [status(thm)], [d32])).
% 41.30/11.04 cnf(d34, plain, singleton(sK58) != X0 | ~in(X1,X0) | in(sK14(sK59,X1),'relation$udom'(sK59)) | ~'Ts9'(sK59), inference(superposition, [status(thm)], [c66,c13])).
% 41.30/11.04 cnf(d35, plain, singleton(sK58) != X0 | ~in(X1,X0) | in(sK14(sK59,X1),'relation$udom'(sK59)), inference(resolution, [status(thm)], [d11,d34])).
% 41.30/11.04 cnf(d36, plain, ~in(X0,singleton(sK58)) | in(sK14(sK59,X0),'relation$udom'(sK59)), inference(equality_resolution, [status(thm)], [d35])).
% 41.30/11.04 cnf(d37, plain, sK58 = apply(sK60,sK14(sK59,X0)) | ~in(X0,singleton(sK58)), inference(resolution, [status(thm)], [d22,d36])).
% 41.30/11.04 cnf(d38, plain, sK58 = apply(sK60,sK14(sK59,sK58)), inference(resolution, [status(thm)], [d37,d33])).
% 41.30/11.04 cnf(d39, plain, in(sK19(X0),X0) | empty(X0), inference(resolution, [status(thm)], [c49,c18])).
% 41.30/11.04 cnf(d40, plain, empty('relation$udom'(sK59)) | sK58 = apply(sK60,sK19('relation$udom'(sK59))), inference(resolution, [status(thm)], [d39,d22])).
% 41.30/11.04 cnf(d41, plain, ~empty('relation$udom'(sK59)) | empty(sK60) | ~relation(sK60), inference(superposition, [status(thm)], [c64,c27])).
% 41.30/11.04 cnf(d42, plain, ~empty('relation$udom'(sK59)) | empty(sK60), inference(resolution, [status(thm)], [c62,d41])).
% 41.30/11.04 cnf(d43, plain, empty(singleton(sK58)) | ~empty(sK60), inference(superposition, [status(thm)], [c65,c31])).
% 41.30/11.04 cnf(d44, plain, ~empty(sK60), inference(resolution, [status(thm)], [c24,d43])).
% 41.30/11.04 cnf(d45, plain, ~empty('relation$udom'(sK59)), inference(resolution, [status(thm)], [d44,d42])).
% 41.30/11.04 cnf(d46, plain, sK58 = apply(sK60,sK19('relation$udom'(sK59))), inference(resolution, [status(thm)], [d45,d40])).
% 41.30/11.04 cnf(d47, plain, sK58 = apply(sK60,sK14(sK59,apply(sK60,X0))) | ~in(X0,'relation$udom'(sK59)), inference(resolution, [status(thm)], [d37,d21])).
% 41.30/11.04 cnf(d48, plain, empty('relation$udom'(sK59)) | sK58 = apply(sK60,sK14(sK59,apply(sK60,sK19('relation$udom'(sK59))))), inference(resolution, [status(thm)], [d39,d47])).
% 41.30/11.04 cnf(d49, plain, sK58 = apply(sK60,sK14(sK59,sK58)) | empty('relation$udom'(sK59)), inference(demodulation, [status(thm)], [d48,d46])).
% 41.30/11.04 cnf(d50, plain, sK58 = sK58 | empty('relation$udom'(sK59)), inference(demodulation, [status(thm)], [d49,d38])).
% 41.30/11.04 cnf(d51, plain, sK58 = sK58, inference(resolution, [status(thm)], [d45,d50])).
% 41.30/11.04 cnf(d52, plain, 'relation$udom'(sK59) != 'relation$udom'(sK59), inference(resolution, [status(thm)], [d51,d31])).
% 41.30/11.04 cnf(d53, plain, $false, inference(equality_resolution, [status(thm)], [d52])).
% 41.30/11.04 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------