%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:41:10 AM UTC 2026
% Result : Theorem 70.50s 23.13s
% Output : CNFRefutation 70.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:44:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.50/23.13 % SZS status Theorem for theBenchmark.p
% 70.50/23.13 % SZS output start CNFRefutation for theBenchmark.p
% 70.50/23.13 fof(commutativity_k2_xboole_0, axiom, ! [X0] : ! [X1] : 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0)).
% 70.50/23.13 fof(commutativity_k3_xboole_0, axiom, ! [X0] : ! [X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0)).
% 70.50/23.13 fof(d10_xboole_0, axiom, ! [X0] : ! [X1] : ((X0 = X1 <=> (subset(X0,X1) & subset(X1,X0))))).
% 70.50/23.13 fof(d1_xboole_0, axiom, ! [X0] : ((X0 = 'empty$uset' <=> ! [X1] : ~in(X1,X0)))).
% 70.50/23.13 fof(d2_subset_1, axiom, ! [X0] : ! [X1] : (((~empty(X0) => (element(X1,X0) <=> in(X1,X0))) & (empty(X0) => (element(X1,X0) <=> empty(X1)))))).
% 70.50/23.13 fof(d7_xboole_0, axiom, ! [X0] : ! [X1] : ((disjoint(X0,X1) <=> 'set$uintersection2'(X0,X1) = 'empty$uset'))).
% 70.50/23.13 fof(d8_setfam_1, axiom, ! [X0] : ! [X1] : ((element(X1,powerset(powerset(X0))) => ! [X2] : ((element(X2,powerset(powerset(X0))) => (X2 = 'complements$uof$usubsets'(X0,X1) <=> ! [X3] : ((element(X3,powerset(X0)) => (in(X3,X2) <=> in('subset$ucomplement'(X0,X3),X1)))))))))).
% 70.50/23.13 fof(existence_m1_subset_1, axiom, ! [X0] : ? [X1] : element(X1,X0)).
% 70.50/23.13 fof(fc1_subset_1, axiom, ! [X0] : ~empty(powerset(X0))).
% 70.50/23.13 fof(idempotence_k3_xboole_0, axiom, ! [X0] : ! [X1] : 'set$uintersection2'(X0,X0) = X0).
% 70.50/23.13 fof(involutiveness_k7_setfam_1, axiom, ! [X0] : ! [X1] : ((element(X1,powerset(powerset(X0))) => 'complements$uof$usubsets'(X0,'complements$uof$usubsets'(X0,X1)) = X1))).
% 70.50/23.13 fof(l25_zfmisc_1, lemma, ! [X0] : ! [X1] : ~((disjoint(singleton(X0),X1) & in(X0,X1)))).
% 70.50/23.13 fof(l32_xboole_1, lemma, ! [X0] : ! [X1] : (('set$udifference'(X0,X1) = 'empty$uset' <=> subset(X0,X1)))).
% 70.50/23.13 fof(l3_subset_1, lemma, ! [X0] : ! [X1] : ((element(X1,powerset(X0)) => ! [X2] : ((in(X2,X1) => in(X2,X0)))))).
% 70.50/23.13 fof(rc2_subset_1, axiom, ! [X0] : ? [X1] : ((element(X1,powerset(X0)) & empty(X1)))).
% 70.50/23.13 fof(reflexivity_r1_tarski, axiom, ! [X0] : ! [X1] : subset(X0,X0)).
% 70.50/23.13 fof(symmetry_r1_xboole_0, axiom, ! [X0] : ! [X1] : ((disjoint(X0,X1) => disjoint(X1,X0)))).
% 70.50/23.13 fof(t17_xboole_1, lemma, ! [X0] : ! [X1] : subset('set$uintersection2'(X0,X1),X0)).
% 70.50/23.13 fof(t2_boole, axiom, ! [X0] : 'set$uintersection2'(X0,'empty$uset') = 'empty$uset').
% 70.50/23.13 fof(t2_tarski, axiom, ! [X0] : ! [X1] : ((! [X2] : ((in(X2,X0) <=> in(X2,X1))) => X0 = X1))).
% 70.50/23.13 fof(t39_xboole_1, lemma, ! [X0] : ! [X1] : 'set$uunion2'(X0,'set$udifference'(X1,X0)) = 'set$uunion2'(X0,X1)).
% 70.50/23.13 fof(t3_subset, axiom, ! [X0] : ! [X1] : ((element(X0,powerset(X1)) <=> subset(X0,X1)))).
% 70.50/23.13 fof(t45_xboole_1, lemma, ! [X0] : ! [X1] : ((subset(X0,X1) => X1 = 'set$uunion2'(X0,'set$udifference'(X1,X0))))).
% 70.50/23.13 fof(t63_xboole_1, lemma, ! [X0] : ! [X1] : ! [X2] : (((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2)))).
% 70.50/23.13 fof(t6_boole, axiom, ! [X0] : ((empty(X0) => X0 = 'empty$uset'))).
% 70.50/23.13 fof(t7_xboole_1, lemma, ! [X0] : ! [X1] : subset(X0,'set$uunion2'(X0,X1))).
% 70.50/23.13 fof(t46_setfam_1, conjecture, ! [X0] : ! [X1] : ((element(X1,powerset(powerset(X0))) => ~((X1 != 'empty$uset' & 'complements$uof$usubsets'(X0,X1) = 'empty$uset'))))).
% 70.50/23.13 fof(negated_conjecture, negated_conjecture, ~! [X0] : ! [X1] : ((element(X1,powerset(powerset(X0))) => ~((X1 != 'empty$uset' & 'complements$uof$usubsets'(X0,X1) = 'empty$uset')))), inference(negate_conjecture, [status(cth)], [t46_setfam_1])).
% 70.50/23.13 cnf(c3, plain, 'set$uunion2'(X0,X1) = 'set$uunion2'(X1,X0), inference(clausification, [status(esa)], [commutativity_k2_xboole_0])).
% 70.50/23.13 cnf(c4, plain, 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0), inference(clausification, [status(esa)], [commutativity_k3_xboole_0])).
% 70.50/23.13 cnf(c7, plain, X0 = X1 | ~subset(X0,X1) | ~subset(X1,X0), inference(clausification, [status(esa)], [d10_xboole_0])).
% 70.50/23.13 cnf(c14, plain, X0 != 'empty$uset' | ~in(X1,X0), inference(clausification, [status(esa)], [d1_xboole_0])).
% 70.50/23.13 cnf(c15, plain, X0 = 'empty$uset' | in(sK18(X0),X0), inference(clausification, [status(esa)], [d1_xboole_0])).
% 70.50/23.13 cnf(c23, plain, empty(X0) | element(X1,X0) | ~in(X1,X0), inference(clausification, [status(esa)], [d2_subset_1])).
% 70.50/23.13 cnf(c101, plain, disjoint(X0,X1) | 'set$uintersection2'(X0,X1) != 'empty$uset', inference(clausification, [status(esa)], [d7_xboole_0])).
% 70.50/23.13 cnf(c103, plain, ~element(X0,powerset(powerset(X1))) | ~element(X2,powerset(powerset(X1))) | X2 = 'complements$uof$usubsets'(X1,X0) | ~X3(X1,X0,X2), inference(clausification, [status(esa)], [d8_setfam_1])).
% 70.50/23.13 cnf(c108, plain, X0(X1,X2,X3) | in(sK87(X1,X2,X3),X3) | in('subset$ucomplement'(X1,sK87(X1,X2,X3)),X2), inference(clausification, [status(esa)], [d8_setfam_1])).
% 70.50/23.13 cnf(c116, plain, element(sK95(X0),X0), inference(clausification, [status(esa)], [existence_m1_subset_1])).
% 70.50/23.13 cnf(c117, plain, ~empty(powerset(X0)), inference(clausification, [status(esa)], [fc1_subset_1])).
% 70.50/23.13 cnf(c123, plain, 'set$uintersection2'(X0,X0) = X0, inference(clausification, [status(esa)], [idempotence_k3_xboole_0])).
% 70.50/23.13 cnf(c125, plain, ~element(X0,powerset(powerset(X1))) | 'complements$uof$usubsets'(X1,'complements$uof$usubsets'(X1,X0)) = X0, inference(clausification, [status(esa)], [involutiveness_k7_setfam_1])).
% 70.50/23.13 cnf(c129, plain, ~disjoint(singleton(X0),X1) | ~in(X0,X1), inference(clausification, [status(esa)], [l25_zfmisc_1])).
% 70.50/23.13 cnf(c134, plain, 'set$udifference'(X0,X1) = 'empty$uset' | ~subset(X0,X1), inference(clausification, [status(esa)], [l32_xboole_1])).
% 70.50/23.13 cnf(c135, plain, ~element(X0,powerset(X1)) | ~in(X2,X0) | in(X2,X1), inference(clausification, [status(esa)], [l3_subset_1])).
% 70.50/23.13 cnf(c149, plain, element(sK145(X0),powerset(X0)), inference(clausification, [status(esa)], [rc2_subset_1])).
% 70.50/23.13 cnf(c150, plain, empty(sK145(X0)), inference(clausification, [status(esa)], [rc2_subset_1])).
% 70.50/23.13 cnf(c152, plain, subset(X0,X0), inference(clausification, [status(esa)], [reflexivity_r1_tarski])).
% 70.50/23.13 cnf(c153, plain, ~disjoint(X0,X1) | disjoint(X1,X0), inference(clausification, [status(esa)], [symmetry_r1_xboole_0])).
% 70.50/23.13 cnf(c166, plain, subset('set$uintersection2'(X0,X1),X0), inference(clausification, [status(esa)], [t17_xboole_1])).
% 70.50/23.13 cnf(c174, plain, 'set$uintersection2'(X0,'empty$uset') = 'empty$uset', inference(clausification, [status(esa)], [t2_boole])).
% 70.50/23.13 cnf(c177, plain, in(sK195(X0,X1),X0) | in(sK195(X0,X1),X1) | X0 = X1, inference(clausification, [status(esa)], [t2_tarski])).
% 70.50/23.13 cnf(c192, plain, 'set$uunion2'(X0,'set$udifference'(X1,X0)) = 'set$uunion2'(X0,X1), inference(clausification, [status(esa)], [t39_xboole_1])).
% 70.50/23.13 cnf(c197, plain, ~element(X0,powerset(X1)) | subset(X0,X1), inference(clausification, [status(esa)], [t3_subset])).
% 70.50/23.13 cnf(c206, plain, ~subset(X0,X1) | X1 = 'set$uunion2'(X0,'set$udifference'(X1,X0)), inference(clausification, [status(esa)], [t45_xboole_1])).
% 70.50/23.13 cnf(c217, plain, ~subset(X0,X1) | ~disjoint(X1,X2) | disjoint(X0,X2), inference(clausification, [status(esa)], [t63_xboole_1])).
% 70.50/23.13 cnf(c221, plain, ~empty(X0) | X0 = 'empty$uset', inference(clausification, [status(esa)], [t6_boole])).
% 70.50/23.13 cnf(c224, plain, subset(X0,'set$uunion2'(X0,X1)), inference(clausification, [status(esa)], [t7_xboole_1])).
% 70.50/23.13 cnf(c238, plain, element(sK293,powerset(powerset(sK292))), inference(clausification, [status(esa)], [negated_conjecture])).
% 70.50/23.13 cnf(c239, plain, sK293 != 'empty$uset', inference(clausification, [status(esa)], [negated_conjecture])).
% 70.50/23.13 cnf(c240, plain, 'complements$uof$usubsets'(sK292,sK293) = 'empty$uset', inference(clausification, [status(esa)], [negated_conjecture])).
% 70.50/23.13 cnf(d0, plain, sK145(X0) = 'empty$uset', inference(resolution, [status(thm)], [c221,c150])).
% 70.50/23.13 cnf(d1, plain, element('empty$uset',powerset(X0)), inference(demodulation, [status(thm)], [c149,d0])).
% 70.50/23.13 cnf(d2, plain, X0 = 'complements$uof$usubsets'(X1,'empty$uset') | ~element(X0,powerset(powerset(X1))) | ~'Ts82'(X1,'empty$uset',X0), inference(resolution, [status(thm)], [c103,d1])).
% 70.50/23.13 cnf(d3, plain, 'empty$uset' = 'complements$uof$usubsets'(X0,'empty$uset') | ~'Ts82'(X0,'empty$uset','empty$uset'), inference(resolution, [status(thm)], [d2,d1])).
% 70.50/23.13 cnf(d4, plain, ~in(X0,'empty$uset'), inference(equality_resolution, [status(thm)], [c14])).
% 70.50/23.13 cnf(d5, plain, X0 = 'empty$uset' | in(sK195(X0,'empty$uset'),X0), inference(resolution, [status(thm)], [c177,d4])).
% 70.50/23.13 cnf(d6, plain, 'set$uintersection2'('empty$uset',X0) = 'empty$uset', inference(superposition, [status(thm)], [c174,c4])).
% 70.50/23.13 cnf(d7, plain, 'empty$uset' != 'empty$uset' | disjoint('empty$uset',X0), inference(superposition, [status(thm)], [d6,c101])).
% 70.50/23.13 cnf(d8, plain, 'set$udifference'(X0,X0) = 'empty$uset', inference(resolution, [status(thm)], [c134,c152])).
% 70.50/23.13 cnf(d9, plain, 'set$udifference'(X0,'set$uunion2'(X0,X1)) = 'empty$uset', inference(resolution, [status(thm)], [c134,c224])).
% 70.50/23.13 cnf(d10, plain, X1 = 'set$uunion2'(X0,X1) | ~subset(X0,X1), inference(demodulation, [status(thm)], [c206,c192])).
% 70.50/23.13 cnf(d11, plain, in(X0,powerset(sK292)) | ~in(X0,sK293), inference(resolution, [status(thm)], [c135,c238])).
% 70.50/23.13 cnf(d12, plain, ~in(X0,sK293) | element(X0,powerset(sK292)) | empty(powerset(sK292)), inference(resolution, [status(thm)], [d11,c23])).
% 70.50/23.13 cnf(d13, plain, ~in(X0,sK293) | element(X0,powerset(sK292)), inference(resolution, [status(thm)], [c117,d12])).
% 70.50/23.13 cnf(d14, plain, subset(X0,sK292) | ~in(X0,sK293), inference(resolution, [status(thm)], [c197,d13])).
% 70.50/23.13 cnf(d15, plain, subset(sK18(sK293),sK292) | sK293 = 'empty$uset', inference(resolution, [status(thm)], [d14,c15])).
% 70.50/23.13 cnf(d16, plain, subset(sK18(sK293),sK292), inference(resolution, [status(thm)], [c239,d15])).
% 70.50/23.13 cnf(d17, plain, sK292 = 'set$uunion2'(sK18(sK293),sK292), inference(resolution, [status(thm)], [d16,d10])).
% 70.50/23.13 cnf(d18, plain, sK292 = 'set$uunion2'(sK292,sK18(sK293)), inference(demodulation, [status(thm)], [d17,c3])).
% 70.50/23.13 cnf(d19, plain, 'set$udifference'(sK292,sK292) = 'empty$uset', inference(superposition, [status(thm)], [d18,d9])).
% 70.50/23.13 cnf(d20, plain, 'empty$uset' = 'empty$uset', inference(demodulation, [status(thm)], [d19,d8])).
% 70.50/23.13 cnf(d21, plain, disjoint('empty$uset',X0), inference(resolution, [status(thm)], [d20,d7])).
% 70.50/23.13 cnf(d22, plain, ~subset(X0,'empty$uset') | disjoint(X0,X1), inference(resolution, [status(thm)], [d21,c217])).
% 70.50/23.13 cnf(d23, plain, subset(sK95(powerset(X0)),X0), inference(resolution, [status(thm)], [c197,c116])).
% 70.50/23.13 cnf(d24, plain, disjoint(sK95(powerset('empty$uset')),X0), inference(resolution, [status(thm)], [d23,d22])).
% 70.50/23.13 cnf(d25, plain, disjoint(X0,sK95(powerset('empty$uset'))), inference(resolution, [status(thm)], [d24,c153])).
% 70.50/23.13 cnf(d26, plain, ~in(X0,sK95(powerset('empty$uset'))), inference(resolution, [status(thm)], [d25,c129])).
% 70.50/23.13 cnf(d27, plain, sK95(powerset('empty$uset')) = 'empty$uset', inference(resolution, [status(thm)], [d26,d5])).
% 70.50/23.13 cnf(d28, plain, in('subset$ucomplement'(X0,sK87(X0,X1,'empty$uset')),X1) | 'Ts82'(X0,X1,'empty$uset'), inference(resolution, [status(thm)], [c108,d4])).
% 70.50/23.13 cnf(d29, plain, 'Ts82'(X0,sK95(powerset('empty$uset')),'empty$uset'), inference(resolution, [status(thm)], [d26,d28])).
% 70.50/23.13 cnf(d30, plain, 'Ts82'(X0,'empty$uset','empty$uset'), inference(demodulation, [status(thm)], [d29,d27])).
% 70.50/23.13 cnf(d31, plain, 'empty$uset' = 'complements$uof$usubsets'(X0,'empty$uset'), inference(resolution, [status(thm)], [d30,d3])).
% 70.50/23.13 cnf(d32, plain, 'complements$uof$usubsets'(sK292,'complements$uof$usubsets'(sK292,sK293)) = sK293, inference(resolution, [status(thm)], [c125,c238])).
% 70.50/23.13 cnf(d33, plain, 'complements$uof$usubsets'(sK292,'empty$uset') = sK293, inference(demodulation, [status(thm)], [d32,c240])).
% 70.50/23.13 cnf(d34, plain, 'empty$uset' = sK293, inference(demodulation, [status(thm)], [d33,d31])).
% 70.50/23.13 cnf(d35, plain, 'empty$uset' != 'empty$uset', inference(demodulation, [status(thm)], [c239,d34])).
% 70.50/23.13 cnf(d36, plain, X0 = 'set$uintersection2'(X0,X1) | ~subset(X0,'set$uintersection2'(X0,X1)), inference(resolution, [status(thm)], [c166,c7])).
% 70.50/23.13 cnf(d37, plain, ~subset(X0,X0) | X0 = 'set$uintersection2'(X0,X0), inference(superposition, [status(thm)], [c123,d36])).
% 70.50/23.13 cnf(d38, plain, X0 = X0 | ~subset(X0,X0), inference(demodulation, [status(thm)], [d37,c123])).
% 70.50/23.13 cnf(d39, plain, X0 = X0, inference(resolution, [status(thm)], [c152,d38])).
% 70.50/23.13 cnf(d40, plain, $false, inference(resolution, [status(thm)], [d39,d35])).
% 70.50/23.13 % SZS output end CNFRefutation for theBenchmark.p
%------------------------------------------------------------------------------