%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG030-10 : 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 06:47:06 AM UTC 2026
% Result : Unsatisfiable 10.62s 7.76s
% Output : CNFRefutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 33 RR)
% Number of literals : 60 ( 59 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 43 ( 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(ax1,axiom,
ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true ).
cnf(ax3_2,axiom,
op1('sK2$uax3$uU','sK1$uax3$uV') != op1('sK1$uax3$uV','sK2$uax3$uU') ).
cnf(ax3_1,axiom,
sorti1('sK1$uax3$uV') = true ).
cnf(ax3,axiom,
sorti1('sK2$uax3$uU') = true ).
cnf(ax4,axiom,
ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1) ).
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_2,negated_conjecture,
ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0 ).
cnf(co1_4,negated_conjecture,
ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op1(j(X1),j(X0)),j(op2(X1,X0))),j(op2(X1,X0))) = j(op2(X1,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(c2,plain,
ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true,
inference(clausification,[status(esa)],[ax1]) ).
cnf(c4,plain,
op1('sK2$uax3$uU','sK1$uax3$uV') != op1('sK1$uax3$uV','sK2$uax3$uU'),
inference(clausification,[status(esa)],[ax3_2]) ).
cnf(c5,plain,
sorti1('sK1$uax3$uV') = true,
inference(clausification,[status(esa)],[ax3_1]) ).
cnf(c6,plain,
sorti1('sK2$uax3$uU') = true,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c7,plain,
ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
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(c10,plain,
ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(clausification,[status(esa)],[co1_2]) ).
cnf(c12,plain,
ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op1(j(X1),j(X0)),j(op2(X1,X0))),j(op2(X1,X0))) = j(op2(X1,X0)),
inference(clausification,[status(esa)],[co1_4]) ).
cnf(d0,plain,
ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),h('sK1$uax3$uV')),h(op1(X0,'sK1$uax3$uV'))),h(op1(X0,'sK1$uax3$uV'))) = h(op1(X0,'sK1$uax3$uV')),
inference(superposition,[status(thm)],[c5,c9]) ).
cnf(d1,plain,
ifeq2(sorti1(X0),true,op2(h(X0),h('sK1$uax3$uV')),h(op1(X0,'sK1$uax3$uV'))) = h(op1(X0,'sK1$uax3$uV')),
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq2(true,true,op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')),h(op1('sK2$uax3$uU','sK1$uax3$uV'))) = h(op1('sK2$uax3$uU','sK1$uax3$uV')),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')) = h(op1('sK2$uax3$uU','sK1$uax3$uV')),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq2(true,true,j(h('sK2$uax3$uU')),'sK2$uax3$uU') = 'sK2$uax3$uU',
inference(superposition,[status(thm)],[c6,c10]) ).
cnf(d5,plain,
j(h('sK2$uax3$uU')) = 'sK2$uax3$uU',
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq2(true,true,j(h('sK1$uax3$uV')),'sK1$uax3$uV') = 'sK1$uax3$uV',
inference(superposition,[status(thm)],[c5,c10]) ).
cnf(d7,plain,
j(h('sK1$uax3$uV')) = 'sK1$uax3$uV',
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(true,true,sorti2(h('sK1$uax3$uV')),true) = true,
inference(superposition,[status(thm)],[c5,c8]) ).
cnf(d9,plain,
sorti2(h('sK1$uax3$uV')) = true,
inference(demodulation,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
ifeq2(true,true,ifeq2(sorti2(X0),true,op1(j(X0),j(h('sK1$uax3$uV'))),j(op2(X0,h('sK1$uax3$uV')))),j(op2(X0,h('sK1$uax3$uV')))) = j(op2(X0,h('sK1$uax3$uV'))),
inference(superposition,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
ifeq2(sorti2(X0),true,op1(j(X0),j(h('sK1$uax3$uV'))),j(op2(X0,h('sK1$uax3$uV')))) = j(op2(X0,h('sK1$uax3$uV'))),
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq2(sorti2(X0),true,op1(j(X0),'sK1$uax3$uV'),j(op2(X0,h('sK1$uax3$uV')))) = j(op2(X0,h('sK1$uax3$uV'))),
inference(demodulation,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
ifeq(true,true,sorti2(h('sK2$uax3$uU')),true) = true,
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d14,plain,
sorti2(h('sK2$uax3$uU')) = true,
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
ifeq2(true,true,op1(j(h('sK2$uax3$uU')),'sK1$uax3$uV'),j(op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')))) = j(op2(h('sK2$uax3$uU'),h('sK1$uax3$uV'))),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
op1(j(h('sK2$uax3$uU')),'sK1$uax3$uV') = j(op2(h('sK2$uax3$uU'),h('sK1$uax3$uV'))),
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
op1('sK2$uax3$uU','sK1$uax3$uV') = j(op2(h('sK2$uax3$uU'),h('sK1$uax3$uV'))),
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
op1('sK2$uax3$uU','sK1$uax3$uV') = j(h(op1('sK2$uax3$uU','sK1$uax3$uV'))),
inference(demodulation,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),h('sK2$uax3$uU')),h(op1(X0,'sK2$uax3$uU'))),h(op1(X0,'sK2$uax3$uU'))) = h(op1(X0,'sK2$uax3$uU')),
inference(superposition,[status(thm)],[c6,c9]) ).
cnf(d20,plain,
ifeq2(sorti1(X0),true,op2(h(X0),h('sK2$uax3$uU')),h(op1(X0,'sK2$uax3$uU'))) = h(op1(X0,'sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
ifeq2(true,true,op2(h('sK1$uax3$uV'),h('sK2$uax3$uU')),h(op1('sK1$uax3$uV','sK2$uax3$uU'))) = h(op1('sK1$uax3$uV','sK2$uax3$uU')),
inference(superposition,[status(thm)],[c5,d20]) ).
cnf(d22,plain,
op2(h('sK1$uax3$uV'),h('sK2$uax3$uU')) = h(op1('sK1$uax3$uV','sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
ifeq2(sorti2(X0),true,ifeq2(true,true,op2(h('sK2$uax3$uU'),X0),op2(X0,h('sK2$uax3$uU'))),op2(X0,h('sK2$uax3$uU'))) = op2(X0,h('sK2$uax3$uU')),
inference(superposition,[status(thm)],[d14,c7]) ).
cnf(d24,plain,
ifeq2(sorti2(X0),true,op2(h('sK2$uax3$uU'),X0),op2(X0,h('sK2$uax3$uU'))) = op2(X0,h('sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
ifeq2(true,true,op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')),op2(h('sK1$uax3$uV'),h('sK2$uax3$uU'))) = op2(h('sK1$uax3$uV'),h('sK2$uax3$uU')),
inference(superposition,[status(thm)],[d9,d24]) ).
cnf(d26,plain,
op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')) = op2(h('sK1$uax3$uV'),h('sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
op2(h('sK2$uax3$uU'),h('sK1$uax3$uV')) = h(op1('sK1$uax3$uV','sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
h(op1('sK2$uax3$uU','sK1$uax3$uV')) = h(op1('sK1$uax3$uV','sK2$uax3$uU')),
inference(demodulation,[status(thm)],[d27,d3]) ).
cnf(d29,plain,
ifeq(true,true,ifeq(sorti1(X0),true,sorti1(op1(X0,'sK2$uax3$uU')),true),true) = true,
inference(superposition,[status(thm)],[c6,c2]) ).
cnf(d30,plain,
ifeq(sorti1(X0),true,sorti1(op1(X0,'sK2$uax3$uU')),true) = true,
inference(demodulation,[status(thm)],[d29,c1]) ).
cnf(d31,plain,
ifeq(true,true,sorti1(op1('sK1$uax3$uV','sK2$uax3$uU')),true) = true,
inference(superposition,[status(thm)],[c5,d30]) ).
cnf(d32,plain,
sorti1(op1('sK1$uax3$uV','sK2$uax3$uU')) = true,
inference(demodulation,[status(thm)],[d31,c1]) ).
cnf(d33,plain,
ifeq2(true,true,j(h(op1('sK1$uax3$uV','sK2$uax3$uU'))),op1('sK1$uax3$uV','sK2$uax3$uU')) = op1('sK1$uax3$uV','sK2$uax3$uU'),
inference(superposition,[status(thm)],[d32,c10]) ).
cnf(d34,plain,
j(h(op1('sK1$uax3$uV','sK2$uax3$uU'))) = op1('sK1$uax3$uV','sK2$uax3$uU'),
inference(demodulation,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
j(h(op1('sK2$uax3$uU','sK1$uax3$uV'))) = op1('sK1$uax3$uV','sK2$uax3$uU'),
inference(demodulation,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
op1('sK2$uax3$uU','sK1$uax3$uV') = op1('sK1$uax3$uV','sK2$uax3$uU'),
inference(demodulation,[status(thm)],[d35,d18]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[c4,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/5.52 % Computer : n012.cluster.edu
% 0.04/5.52 % Model : x86_64 x86_64
% 0.04/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.52 % Memory : 8046.5625MB
% 0.04/5.52 % OS : Linux 6.8.0-71-generic
% 0.04/5.52 % CPULimit : 300
% 0.04/5.52 % WCLimit : 300
% 0.04/5.52 % DateTime : Sat Sep 26 20:59:27 UTC 2026
% 0.04/5.52 % CPUTime :
% 0.04/5.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.62/7.76 % SZS status Unsatisfiable for theBenchmark.p
% 10.62/7.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------