%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 06:47:21 AM UTC 2026
% Result : Unsatisfiable 32.77s 4.77s
% Output : CNFRefutation 32.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 24 RR)
% Number of literals : 40 ( 39 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 28 ( 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(ax3_1,axiom,
ifeq(sorti1(X0),true,sorti1('sK2$uax3$uV'(X0)),true) = true ).
cnf(ax3,axiom,
ifeq2(sorti1(X0),true,op1('sK2$uax3$uV'(X0),'sK2$uax3$uV'(X0)),X0) = X0 ).
cnf(ax4_1,axiom,
tuple(op2(X0,X0),sorti2(X0)) != tuple('sK1$uax4$uU',true) ).
cnf(ax4,axiom,
sorti2('sK1$uax4$uU') = true ).
cnf(co1,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true ).
cnf(co1_1,negated_conjecture,
ifeq2(sorti1(X0),true,ifeq2(sorti1(X1),true,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))) = h(op1(X1,X0)) ).
cnf(co1_3,negated_conjecture,
ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true ).
cnf(co1_5,negated_conjecture,
ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0 ).
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(c4,plain,
ifeq(sorti1(X0),true,sorti1('sK2$uax3$uV'(X0)),true) = true,
inference(clausification,[status(esa)],[ax3_1]) ).
cnf(c5,plain,
ifeq2(sorti1(X0),true,op1('sK2$uax3$uV'(X0),'sK2$uax3$uV'(X0)),X0) = X0,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c6,plain,
tuple(op2(X0,X0),sorti2(X0)) != tuple('sK1$uax4$uU',true),
inference(clausification,[status(esa)],[ax4_1]) ).
cnf(c7,plain,
sorti2('sK1$uax4$uU') = true,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c8,plain,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(clausification,[status(esa)],[co1]) ).
cnf(c9,plain,
ifeq2(sorti1(X0),true,ifeq2(sorti1(X1),true,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))) = h(op1(X1,X0)),
inference(clausification,[status(esa)],[co1_1]) ).
cnf(c11,plain,
ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(clausification,[status(esa)],[co1_3]) ).
cnf(c13,plain,
ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(clausification,[status(esa)],[co1_5]) ).
cnf(d0,plain,
ifeq(true,true,sorti1(j('sK1$uax4$uU')),true) = true,
inference(superposition,[status(thm)],[c7,c11]) ).
cnf(d1,plain,
sorti1(j('sK1$uax4$uU')) = true,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
ifeq(true,true,sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))),true) = true,
inference(superposition,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))) = true,
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
ifeq(true,true,sorti2(h('sK2$uax3$uV'(j('sK1$uax4$uU')))),true) = true,
inference(superposition,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
sorti2(h('sK2$uax3$uV'(j('sK1$uax4$uU')))) = true,
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
ifeq2(true,true,h(j('sK1$uax4$uU')),'sK1$uax4$uU') = 'sK1$uax4$uU',
inference(superposition,[status(thm)],[c7,c13]) ).
cnf(d7,plain,
h(j('sK1$uax4$uU')) = 'sK1$uax4$uU',
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq2(true,true,op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU'))),j('sK1$uax4$uU')) = j('sK1$uax4$uU'),
inference(superposition,[status(thm)],[d1,c5]) ).
cnf(d9,plain,
op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU'))) = j('sK1$uax4$uU'),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq2(sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))),true,ifeq2(sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))),true,op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))),h(j('sK1$uax4$uU'))),h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU'))))) = h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU')))),
inference(superposition,[status(thm)],[d9,c9]) ).
cnf(d11,plain,
ifeq2(true,true,ifeq2(sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))),true,op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))),h(j('sK1$uax4$uU'))),h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU'))))) = h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU')))),
inference(demodulation,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
ifeq2(sorti1('sK2$uax3$uV'(j('sK1$uax4$uU'))),true,op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))),h(j('sK1$uax4$uU'))) = h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU')))),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
ifeq2(true,true,op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))),h(j('sK1$uax4$uU'))) = h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU')))),
inference(demodulation,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))) = h(op1('sK2$uax3$uV'(j('sK1$uax4$uU')),'sK2$uax3$uV'(j('sK1$uax4$uU')))),
inference(demodulation,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))) = h(j('sK1$uax4$uU')),
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
op2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))),h('sK2$uax3$uV'(j('sK1$uax4$uU')))) = 'sK1$uax4$uU',
inference(demodulation,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
tuple('sK1$uax4$uU',sorti2(h('sK2$uax3$uV'(j('sK1$uax4$uU'))))) != tuple('sK1$uax4$uU',true),
inference(superposition,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
tuple('sK1$uax4$uU',true) != tuple('sK1$uax4$uU',true),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
$false,
inference(equality_resolution,[status(thm)],[d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:08:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.77/4.77 % SZS status Unsatisfiable for theBenchmark.p
% 32.77/4.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------