%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:41:40 AM UTC 2026
% Result : Unsatisfiable 11.97s 3.51s
% Output : CNFRefutation 11.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 26 RR)
% Number of literals : 48 ( 47 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 40 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(fc3_tops_1,axiom,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('closed$usubset'(X0,X1),true,ifeq('topological$uspace'(X1),true,ifeq('top$ustr'(X1),true,'open$usubset'('subset$ucomplement'('the$ucarrier'(X1),X0),X1),true),true),true),true) = true ).
cnf(dt_k3_subset_1,axiom,
ifeq(element(X0,powerset(X1)),true,element('subset$ucomplement'(X1,X0),powerset(X1)),true) = true ).
cnf(dt_k6_pre_topc,axiom,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('top$ustr'(X1),true,element('topstr$uclosure'(X1,X0),powerset('the$ucarrier'(X1))),true),true) = true ).
cnf(fc2_tops_1,axiom,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('topological$uspace'(X1),true,ifeq('top$ustr'(X1),true,'closed$usubset'('topstr$uclosure'(X1,X0),X1),true),true),true) = true ).
cnf(d1_tops_1,axiom,
ifeq2(element(X0,powerset('the$ucarrier'(X1))),true,ifeq2('top$ustr'(X1),true,'subset$ucomplement'('the$ucarrier'(X1),'topstr$uclosure'(X1,'subset$ucomplement'('the$ucarrier'(X1),X0))),interior(X1,X0)),interior(X1,X0)) = interior(X1,X0) ).
cnf(t51_tops_1,negated_conjecture,
'top$ustr'('sK2$ut51$utops$u1$uA') = true ).
cnf(t51_tops_1_1,negated_conjecture,
'topological$uspace'('sK2$ut51$utops$u1$uA') = true ).
cnf(t51_tops_1_2,negated_conjecture,
element('sK1$ut51$utops$u1$uB',powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))) = true ).
cnf(t51_tops_1_3,negated_conjecture,
'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA') != true ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c2,plain,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('closed$usubset'(X0,X1),true,ifeq('topological$uspace'(X1),true,ifeq('top$ustr'(X1),true,'open$usubset'('subset$ucomplement'('the$ucarrier'(X1),X0),X1),true),true),true),true) = true,
inference(clausification,[status(esa)],[fc3_tops_1]) ).
cnf(c8,plain,
ifeq(element(X0,powerset(X1)),true,element('subset$ucomplement'(X1,X0),powerset(X1)),true) = true,
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c9,plain,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('top$ustr'(X1),true,element('topstr$uclosure'(X1,X0),powerset('the$ucarrier'(X1))),true),true) = true,
inference(clausification,[status(esa)],[dt_k6_pre_topc]) ).
cnf(c10,plain,
ifeq(element(X0,powerset('the$ucarrier'(X1))),true,ifeq('topological$uspace'(X1),true,ifeq('top$ustr'(X1),true,'closed$usubset'('topstr$uclosure'(X1,X0),X1),true),true),true) = true,
inference(clausification,[status(esa)],[fc2_tops_1]) ).
cnf(c20,plain,
ifeq2(element(X0,powerset('the$ucarrier'(X1))),true,ifeq2('top$ustr'(X1),true,'subset$ucomplement'('the$ucarrier'(X1),'topstr$uclosure'(X1,'subset$ucomplement'('the$ucarrier'(X1),X0))),interior(X1,X0)),interior(X1,X0)) = interior(X1,X0),
inference(clausification,[status(esa)],[d1_tops_1]) ).
cnf(c21,plain,
'top$ustr'('sK2$ut51$utops$u1$uA') = true,
inference(clausification,[status(esa)],[t51_tops_1]) ).
cnf(c22,plain,
'topological$uspace'('sK2$ut51$utops$u1$uA') = true,
inference(clausification,[status(esa)],[t51_tops_1_1]) ).
cnf(c23,plain,
element('sK1$ut51$utops$u1$uB',powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))) = true,
inference(clausification,[status(esa)],[t51_tops_1_2]) ).
cnf(c24,plain,
'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA') != true,
inference(clausification,[status(esa)],[t51_tops_1_3]) ).
cnf(d0,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq(true,true,ifeq('top$ustr'('sK2$ut51$utops$u1$uA'),true,'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA',X0),'sK2$ut51$utops$u1$uA'),true),true),true) = true,
inference(superposition,[status(thm)],[c22,c10]) ).
cnf(d1,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('top$ustr'('sK2$ut51$utops$u1$uA'),true,'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA',X0),'sK2$ut51$utops$u1$uA'),true),true) = true,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq(true,true,'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA',X0),'sK2$ut51$utops$u1$uA'),true),true) = true,
inference(demodulation,[status(thm)],[d1,c21]) ).
cnf(d3,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA',X0),'sK2$ut51$utops$u1$uA'),true) = true,
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
ifeq(true,true,element('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true) = true,
inference(superposition,[status(thm)],[c23,c8]) ).
cnf(d5,plain,
element('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))) = true,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
ifeq(true,true,'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),'sK2$ut51$utops$u1$uA'),true) = true,
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
'closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),'sK2$ut51$utops$u1$uA') = true,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
ifeq(true,true,ifeq('top$ustr'('sK2$ut51$utops$u1$uA'),true,element('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true),true) = true,
inference(superposition,[status(thm)],[d5,c9]) ).
cnf(d9,plain,
ifeq('top$ustr'('sK2$ut51$utops$u1$uA'),true,element('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true) = true,
inference(demodulation,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
ifeq(true,true,element('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true) = true,
inference(demodulation,[status(thm)],[d9,c21]) ).
cnf(d11,plain,
element('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))) = true,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('closed$usubset'(X0,'sK2$ut51$utops$u1$uA'),true,ifeq('topological$uspace'('sK2$ut51$utops$u1$uA'),true,ifeq(true,true,'open$usubset'('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),X0),'sK2$ut51$utops$u1$uA'),true),true),true),true) = true,
inference(superposition,[status(thm)],[c21,c2]) ).
cnf(d13,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('closed$usubset'(X0,'sK2$ut51$utops$u1$uA'),true,ifeq(true,true,ifeq(true,true,'open$usubset'('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),X0),'sK2$ut51$utops$u1$uA'),true),true),true),true) = true,
inference(demodulation,[status(thm)],[d12,c22]) ).
cnf(d14,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('closed$usubset'(X0,'sK2$ut51$utops$u1$uA'),true,ifeq(true,true,'open$usubset'('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),X0),'sK2$ut51$utops$u1$uA'),true),true),true) = true,
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
ifeq(element(X0,powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('closed$usubset'(X0,'sK2$ut51$utops$u1$uA'),true,'open$usubset'('subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),X0),'sK2$ut51$utops$u1$uA'),true),true) = true,
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
ifeq2(true,true,ifeq2('top$ustr'('sK2$ut51$utops$u1$uA'),true,'subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'))),interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB')),interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB')) = interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),
inference(superposition,[status(thm)],[c23,c20]) ).
cnf(d17,plain,
ifeq2('top$ustr'('sK2$ut51$utops$u1$uA'),true,'subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'))),interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB')) = interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
ifeq2(true,true,'subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'))),interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB')) = interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),
inference(demodulation,[status(thm)],[d17,c21]) ).
cnf(d19,plain,
'subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB'))) = interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
ifeq(element('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),powerset('the$ucarrier'('sK2$ut51$utops$u1$uA'))),true,ifeq('closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),'sK2$ut51$utops$u1$uA'),true,'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA'),true),true) = true,
inference(superposition,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
ifeq(true,true,ifeq('closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),'sK2$ut51$utops$u1$uA'),true,'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA'),true),true) = true,
inference(demodulation,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
ifeq('closed$usubset'('topstr$uclosure'('sK2$ut51$utops$u1$uA','subset$ucomplement'('the$ucarrier'('sK2$ut51$utops$u1$uA'),'sK1$ut51$utops$u1$uB')),'sK2$ut51$utops$u1$uA'),true,'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA'),true) = true,
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
ifeq(true,true,'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA'),true) = true,
inference(demodulation,[status(thm)],[d22,d7]) ).
cnf(d24,plain,
'open$usubset'(interior('sK2$ut51$utops$u1$uA','sK1$ut51$utops$u1$uB'),'sK2$ut51$utops$u1$uA') = true,
inference(demodulation,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[c24,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU323-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 09:12:05 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.97/3.51 % SZS status Unsatisfiable for theBenchmark.p
% 11.97/3.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------