%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:33:41 AM UTC 2026
% Result : Theorem 30.71s 17.87s
% Output : CNFRefutation 30.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.32 % Computer : n012.cluster.edu
% 0.03/10.32 % Model : x86_64 x86_64
% 0.03/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.32 % Memory : 8046.5625MB
% 0.03/10.32 % OS : Linux 6.8.0-71-generic
% 0.03/10.33 % CPULimit : 300
% 0.03/10.33 % WCLimit : 300
% 0.03/10.33 % DateTime : Sat Sep 26 08:29:46 UTC 2026
% 0.03/10.33 % CPUTime :
% 0.03/10.33 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.71/17.87 % SZS status Theorem for theBenchmark.p
% 30.71/17.87 % SZS output start CNFRefutation for theBenchmark.p
% 30.71/17.87 fof(d1_tarski, axiom, ! [X0] : ! [X1] : ((X1 = singleton(X0) <=> ! [X2] : ((in(X2,X1) <=> X2 = X0))))).
% 30.71/17.87 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)))))))))).
% 30.71/17.87 fof(existence_m1_subset_1, axiom, ! [X0] : ? [X1] : element(X1,X0)).
% 30.71/17.87 fof(fc2_subset_1, axiom, ! [X0] : ~empty(singleton(X0))).
% 30.71/17.87 fof(fc6_relat_1, axiom, ! [X0] : (((~empty(X0) & relation(X0)) => ~empty('relation$urng'(X0))))).
% 30.71/17.87 fof(fc7_relat_1, axiom, ! [X0] : ((empty(X0) => (empty('relation$udom'(X0)) & relation('relation$udom'(X0)))))).
% 30.71/17.87 fof(t2_subset, axiom, ! [X0] : ! [X1] : ((element(X0,X1) => (empty(X1) | in(X0,X1))))).
% 30.71/17.87 fof(t7_boole, axiom, ! [X0] : ! [X1] : ~((in(X0,X1) & empty(X1)))).
% 30.71/17.87 fof(t14_funct_1, conjecture, ! [X0] : ! [X1] : (((relation(X1) & function(X1)) => ('relation$udom'(X1) = singleton(X0) => 'relation$urng'(X1) = singleton(apply(X1,X0)))))).
% 30.71/17.87 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : (((relation(X1) & function(X1)) => ('relation$udom'(X1) = singleton(X0) => 'relation$urng'(X1) = singleton(apply(X1,X0))))), inference(negate_conjecture, [status(cth)], [t14_funct_1])).
% 30.71/17.87 cnf(c3, plain, singleton(X0) != X1 | ~in(X2,X1) | X0 = X2, inference(clausification, [status(esa)], [d1_tarski])).
% 30.71/17.87 cnf(c4, plain, singleton(X0) != X1 | in(X2,X1) | X0 != X2, inference(clausification, [status(esa)], [d1_tarski])).
% 30.71/17.87 cnf(c6, plain, singleton(X0) = X1 | in(sK7(X0,X1),X1) | X0 = sK7(X0,X1), inference(clausification, [status(esa)], [d1_tarski])).
% 30.71/17.87 cnf(c7, plain, singleton(X0) = X1 | X0 != sK7(X0,X1) | ~in(sK7(X0,X1),X1), inference(clausification, [status(esa)], [d1_tarski])).
% 30.71/17.87 cnf(c9, plain, ~function(X0) | ~relation(X0) | X1(X0), inference(clausification, [status(esa)], [d5_funct_1])).
% 30.71/17.87 cnf(c13, plain, ~X0(X1) | 'relation$urng'(X1) != X2 | ~in(X3,X2) | in(sK14(X1,X3),'relation$udom'(X1)), inference(clausification, [status(esa)], [d5_funct_1])).
% 30.71/17.87 cnf(c14, plain, ~X0(X1) | 'relation$urng'(X1) != X2 | ~in(X3,X2) | apply(X1,sK14(X1,X3)) = X3, inference(clausification, [status(esa)], [d5_funct_1])).
% 30.71/17.87 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])).
% 30.71/17.87 cnf(c18, plain, element(sK19(X0),X0), inference(clausification, [status(esa)], [existence_m1_subset_1])).
% 30.71/17.87 cnf(c24, plain, ~empty(singleton(X0)), inference(clausification, [status(esa)], [fc2_subset_1])).
% 30.71/17.87 cnf(c28, plain, ~relation(X0) | empty(X0) | ~empty('relation$urng'(X0)), inference(clausification, [status(esa)], [fc6_relat_1])).
% 30.71/17.87 cnf(c29, plain, ~empty(X0) | empty('relation$udom'(X0)), inference(clausification, [status(esa)], [fc7_relat_1])).
% 30.71/17.87 cnf(c49, plain, ~element(X0,X1) | in(X0,X1) | empty(X1), inference(clausification, [status(esa)], [t2_subset])).
% 30.71/17.87 cnf(c59, plain, ~in(X0,X1) | ~empty(X1), inference(clausification, [status(esa)], [t7_boole])).
% 30.71/17.87 cnf(c61, plain, function(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 30.71/17.87 cnf(c62, plain, relation(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 30.71/17.87 cnf(c63, plain, singleton(apply(sK59,sK58)) != 'relation$urng'(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 30.71/17.87 cnf(c64, plain, singleton(sK58) = 'relation$udom'(sK59), inference(clausification, [status(esa)], [negated_conjecture])).
% 30.71/17.87 cnf(d0, plain, ~function(sK59) | 'Ts9'(sK59), inference(resolution, [status(thm)], [c9,c62])).
% 30.71/17.87 cnf(d1, plain, 'Ts9'(sK59), inference(resolution, [status(thm)], [c61,d0])).
% 30.71/17.87 cnf(d2, plain, apply(X0,sK14(X0,X1)) = X1 | ~in(X1,'relation$urng'(X0)) | ~'Ts9'(X0), inference(equality_resolution, [status(thm)], [c14])).
% 30.71/17.87 cnf(d3, plain, apply(X0,sK14(X0,sK7(X1,'relation$urng'(X0)))) = sK7(X1,'relation$urng'(X0)) | ~'Ts9'(X0) | X1 = sK7(X1,'relation$urng'(X0)) | singleton(X1) = 'relation$urng'(X0), inference(resolution, [status(thm)], [d2,c6])).
% 30.71/17.87 cnf(d4, plain, X0 = sK7(X0,'relation$urng'(sK59)) | singleton(X0) = 'relation$urng'(sK59) | apply(sK59,sK14(sK59,sK7(X0,'relation$urng'(sK59)))) = sK7(X0,'relation$urng'(sK59)), inference(resolution, [status(thm)], [d3,d1])).
% 30.71/17.87 cnf(d5, plain, X0 = X1 | ~in(X1,singleton(X0)), inference(equality_resolution, [status(thm)], [c3])).
% 30.71/17.87 cnf(d6, plain, ~in(X0,'relation$urng'(X1)) | in(sK14(X1,X0),'relation$udom'(X1)) | ~'Ts9'(X1), inference(equality_resolution, [status(thm)], [c13])).
% 30.71/17.87 cnf(d7, plain, in(sK14(sK59,X0),singleton(sK58)) | ~in(X0,'relation$urng'(sK59)) | ~'Ts9'(sK59), inference(superposition, [status(thm)], [c64,d6])).
% 30.71/17.87 cnf(d8, plain, ~in(X0,'relation$urng'(sK59)) | in(sK14(sK59,X0),singleton(sK58)), inference(resolution, [status(thm)], [d1,d7])).
% 30.71/17.87 cnf(d9, plain, ~in(X0,'relation$urng'(sK59)) | sK58 = sK14(sK59,X0), inference(resolution, [status(thm)], [d8,d5])).
% 30.71/17.87 cnf(d10, plain, sK58 = sK14(sK59,sK7(X0,'relation$urng'(sK59))) | X0 = sK7(X0,'relation$urng'(sK59)) | singleton(X0) = 'relation$urng'(sK59), inference(resolution, [status(thm)], [d9,c6])).
% 30.71/17.87 cnf(d11, plain, apply(sK59,sK58) = sK7(X0,'relation$urng'(sK59)) | X0 = sK7(X0,'relation$urng'(sK59)) | singleton(X0) = 'relation$urng'(sK59) | X0 = sK7(X0,'relation$urng'(sK59)) | singleton(X0) = 'relation$urng'(sK59), inference(superposition, [status(thm)], [d10,d4])).
% 30.71/17.87 cnf(d12, plain, apply(sK59,sK58) != X0 | X0 = sK7(X0,'relation$urng'(sK59)) | singleton(X0) = 'relation$urng'(sK59), inference(equality_factoring, [status(thm)], [d11])).
% 30.71/17.87 cnf(d13, plain, apply(sK59,sK58) = sK7(apply(sK59,sK58),'relation$urng'(sK59)) | singleton(apply(sK59,sK58)) = 'relation$urng'(sK59), inference(equality_resolution, [status(thm)], [d12])).
% 30.71/17.87 cnf(d14, plain, apply(sK59,sK58) = sK7(apply(sK59,sK58),'relation$urng'(sK59)), inference(resolution, [status(thm)], [c63,d13])).
% 30.71/17.87 cnf(d15, plain, apply(sK59,sK58) != apply(sK59,sK58) | singleton(apply(sK59,sK58)) = 'relation$urng'(sK59) | ~in(sK7(apply(sK59,sK58),'relation$urng'(sK59)),'relation$urng'(sK59)), inference(superposition, [status(thm)], [d14,c7])).
% 30.71/17.87 cnf(d16, plain, singleton(apply(sK59,sK58)) = 'relation$urng'(sK59) | apply(sK59,sK58) != apply(sK59,sK58) | ~in(apply(sK59,sK58),'relation$urng'(sK59)), inference(demodulation, [status(thm)], [d15,d14])).
% 30.71/17.87 cnf(d17, plain, apply(sK59,sK58) != apply(sK59,sK58) | ~in(apply(sK59,sK58),'relation$urng'(sK59)), inference(resolution, [status(thm)], [c63,d16])).
% 30.71/17.87 cnf(d18, plain, X0 != apply(sK59,sK58) | singleton(X0) = 'relation$urng'(sK59) | apply(sK59,sK58) = sK7(X0,'relation$urng'(sK59)), inference(equality_factoring, [status(thm)], [d11])).
% 30.71/17.87 cnf(d19, plain, singleton(apply(sK59,sK58)) = 'relation$urng'(sK59) | apply(sK59,sK58) = sK7(apply(sK59,sK58),'relation$urng'(sK59)), inference(equality_resolution, [status(thm)], [d18])).
% 30.71/17.87 cnf(d20, plain, singleton(apply(sK59,sK58)) = 'relation$urng'(sK59) | apply(sK59,sK58) = apply(sK59,sK58), inference(demodulation, [status(thm)], [d19,d14])).
% 30.71/17.87 cnf(d21, plain, apply(sK59,sK58) = apply(sK59,sK58), inference(resolution, [status(thm)], [c63,d20])).
% 30.71/17.87 cnf(d22, plain, ~in(apply(sK59,sK58),'relation$urng'(sK59)), inference(resolution, [status(thm)], [d21,d17])).
% 30.71/17.87 cnf(d23, plain, in(sK19(X0),X0) | empty(X0), inference(resolution, [status(thm)], [c49,c18])).
% 30.71/17.87 cnf(d24, plain, sK58 = sK14(sK59,sK19('relation$urng'(sK59))) | empty('relation$urng'(sK59)), inference(resolution, [status(thm)], [d9,d23])).
% 30.71/17.87 cnf(d25, plain, sK58 = sK14(sK59,sK19('relation$urng'(sK59))) | empty(sK59) | ~relation(sK59), inference(resolution, [status(thm)], [d24,c28])).
% 30.71/17.87 cnf(d26, plain, sK58 = sK14(sK59,sK19('relation$urng'(sK59))) | empty(sK59), inference(resolution, [status(thm)], [c62,d25])).
% 30.71/17.87 cnf(d27, plain, empty(singleton(sK58)) | ~empty(sK59), inference(superposition, [status(thm)], [c64,c29])).
% 30.71/17.87 cnf(d28, plain, ~empty(sK59), inference(resolution, [status(thm)], [c24,d27])).
% 30.71/17.87 cnf(d29, plain, sK58 = sK14(sK59,sK19('relation$urng'(sK59))), inference(resolution, [status(thm)], [d28,d26])).
% 30.71/17.87 cnf(d30, plain, apply(X0,sK14(X0,sK19('relation$urng'(X0)))) = sK19('relation$urng'(X0)) | ~'Ts9'(X0) | empty('relation$urng'(X0)), inference(resolution, [status(thm)], [d2,d23])).
% 30.71/17.87 cnf(d31, plain, apply(X0,sK14(X0,sK19('relation$urng'(X0)))) = sK19('relation$urng'(X0)) | ~'Ts9'(X0) | empty(X0) | ~relation(X0), inference(resolution, [status(thm)], [d30,c28])).
% 30.71/17.87 cnf(d32, plain, apply(sK59,sK14(sK59,sK19('relation$urng'(sK59)))) = sK19('relation$urng'(sK59)) | empty(sK59) | ~relation(sK59), inference(resolution, [status(thm)], [d31,d1])).
% 30.71/17.87 cnf(d33, plain, apply(sK59,sK58) = sK19('relation$urng'(sK59)) | empty(sK59) | ~relation(sK59), inference(demodulation, [status(thm)], [d32,d29])).
% 30.71/17.87 cnf(d34, plain, apply(sK59,sK58) = sK19('relation$urng'(sK59)) | empty(sK59), inference(resolution, [status(thm)], [c62,d33])).
% 30.71/17.87 cnf(d35, plain, apply(sK59,sK58) = sK19('relation$urng'(sK59)), inference(resolution, [status(thm)], [d28,d34])).
% 30.71/17.87 cnf(d36, plain, in(apply(sK59,sK58),'relation$urng'(sK59)) | empty('relation$urng'(sK59)), inference(superposition, [status(thm)], [d35,d23])).
% 30.71/17.87 cnf(d37, plain, X0 != X1 | in(X1,singleton(X0)), inference(equality_resolution, [status(thm)], [c4])).
% 30.71/17.87 cnf(d38, plain, in(X0,singleton(X0)), inference(equality_resolution, [status(thm)], [d37])).
% 30.71/17.87 cnf(d39, plain, 'relation$urng'(X0) != X1 | in(apply(X0,X2),X1) | ~in(X2,'relation$udom'(X0)) | ~'Ts9'(X0), inference(equality_resolution, [status(thm)], [c15])).
% 30.71/17.87 cnf(d40, plain, ~in(X0,'relation$udom'(X1)) | in(apply(X1,X0),'relation$urng'(X1)) | ~'Ts9'(X1), inference(equality_resolution, [status(thm)], [d39])).
% 30.71/17.87 cnf(d41, plain, ~in(X0,'relation$udom'(X1)) | ~'Ts9'(X1) | ~empty('relation$urng'(X1)), inference(resolution, [status(thm)], [d40,c59])).
% 30.71/17.87 cnf(d42, plain, ~in(X0,singleton(sK58)) | ~empty('relation$urng'(sK59)) | ~'Ts9'(sK59), inference(superposition, [status(thm)], [c64,d41])).
% 30.71/17.87 cnf(d43, plain, ~in(X0,singleton(sK58)) | ~empty('relation$urng'(sK59)), inference(resolution, [status(thm)], [d1,d42])).
% 30.71/17.87 cnf(d44, plain, ~empty('relation$urng'(sK59)), inference(resolution, [status(thm)], [d43,d38])).
% 30.71/17.87 cnf(d45, plain, in(apply(sK59,sK58),'relation$urng'(sK59)), inference(resolution, [status(thm)], [d44,d36])).
% 30.71/17.87 cnf(d46, plain, $false, inference(resolution, [status(thm)], [d45,d22])).
% 30.71/17.87 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------