%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:19:02 AM UTC 2026
% Result : Unsatisfiable 40.34s 6.25s
% Output : CNFRefutation 40.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 11 RR)
% Number of literals : 86 ( 85 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 : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 192 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule1,axiom,
minus(X0,zero) = X0 ).
cnf(rule2,axiom,
minus(s(X0),s(X1)) = minus(X0,X1) ).
cnf(rule3,axiom,
'\'<=\''(zero,X0) = true ).
cnf(rule4,axiom,
'\'<=\''(s(X0),zero) = false ).
cnf(rule5,axiom,
'\'<=\''(s(X0),s(X1)) = '\'<=\''(X0,X1) ).
cnf(rule6,axiom,
if(true,X0,X1) = X0 ).
cnf(rule7,axiom,
if(false,X0,X1) = X1 ).
cnf(rule9,axiom,
perfectp(s(X0)) = f(X0,s(zero),s(X0),s(X0)) ).
cnf(rule10,axiom,
f(zero,X0,zero,X1) = true ).
cnf(rule12,axiom,
f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2) ).
cnf(rule13,axiom,
f(s(X0),s(X1),X2,X3) = if('\'<=\''(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)) ).
cnf(goal,negated_conjecture,
perfectp(X0) != true ).
cnf(c0,plain,
minus(X0,zero) = X0,
inference(clausification,[status(esa)],[rule1]) ).
cnf(c1,plain,
minus(s(X0),s(X1)) = minus(X0,X1),
inference(clausification,[status(esa)],[rule2]) ).
cnf(c2,plain,
'\'<=\''(zero,X0) = true,
inference(clausification,[status(esa)],[rule3]) ).
cnf(c3,plain,
'\'<=\''(s(X0),zero) = false,
inference(clausification,[status(esa)],[rule4]) ).
cnf(c4,plain,
'\'<=\''(s(X0),s(X1)) = '\'<=\''(X0,X1),
inference(clausification,[status(esa)],[rule5]) ).
cnf(c5,plain,
if(true,X0,X1) = X0,
inference(clausification,[status(esa)],[rule6]) ).
cnf(c6,plain,
if(false,X0,X1) = X1,
inference(clausification,[status(esa)],[rule7]) ).
cnf(c8,plain,
perfectp(s(X0)) = f(X0,s(zero),s(X0),s(X0)),
inference(clausification,[status(esa)],[rule9]) ).
cnf(c9,plain,
f(zero,X0,zero,X1) = true,
inference(clausification,[status(esa)],[rule10]) ).
cnf(c11,plain,
f(s(X0),zero,X1,X2) = f(X0,X2,minus(X1,s(X0)),X2),
inference(clausification,[status(esa)],[rule12]) ).
cnf(c12,plain,
f(s(X0),s(X1),X2,X3) = if('\'<=\''(X0,X1),f(s(X0),minus(X1,X0),X2,X3),f(X0,X3,X2,X3)),
inference(clausification,[status(esa)],[rule13]) ).
cnf(c13,plain,
perfectp(X0) != true,
inference(clausification,[status(esa)],[goal]) ).
cnf(d0,plain,
f(s(X1),zero,s(X0),X2) = f(X1,X2,minus(X0,X1),X2),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(d1,plain,
f(s(zero),zero,s(X0),X1) = f(zero,X1,X0,X1),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
f(s(zero),zero,s(zero),X0) = true,
inference(superposition,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
f(s(zero),s(X0),X1,X2) = if(true,f(s(zero),minus(X0,zero),X1,X2),f(zero,X2,X1,X2)),
inference(superposition,[status(thm)],[c2,c12]) ).
cnf(d4,plain,
f(s(zero),s(X0),X1,X2) = f(s(zero),minus(X0,zero),X1,X2),
inference(demodulation,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
f(s(zero),s(X0),X1,X2) = f(s(zero),X0,X1,X2),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
f(s(s(X0)),s(zero),X1,X2) = if(false,f(s(s(X0)),minus(zero,s(X0)),X1,X2),f(s(X0),X2,X1,X2)),
inference(superposition,[status(thm)],[c3,c12]) ).
cnf(d7,plain,
f(s(s(X0)),s(zero),X1,X2) = f(s(X0),X2,X1,X2),
inference(demodulation,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
f(s(s(zero)),s(zero),X1,s(X0)) = f(s(zero),X0,X1,s(X0)),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
f(s(s(zero)),s(zero),X1,s(s(X0))) = f(s(zero),X0,X1,s(s(X0))),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
f(s(s(zero)),s(zero),X1,s(s(s(X0)))) = f(s(zero),X0,X1,s(s(s(X0)))),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(X0))))) = f(s(zero),X0,X1,s(s(s(s(X0))))),
inference(superposition,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(s(X0)))))) = f(s(zero),X0,X1,s(s(s(s(s(X0)))))),
inference(superposition,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(s(s(X0))))))) = f(s(zero),X0,X1,s(s(s(s(s(s(X0))))))),
inference(superposition,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
f(s(zero),s(X0),X1,X2) = if('\'<=\''(zero,X0),f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d15,plain,
f(s(zero),X0,X1,X2) = if('\'<=\''(zero,X0),f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)),
inference(demodulation,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
f(s(zero),X0,X1,X2) = if(true,f(s(zero),X0,X1,X2),f(zero,X2,X1,X2)),
inference(demodulation,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
f(s(zero),X0,X1,X2) = f(s(zero),X0,X1,X2),
inference(demodulation,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
f(s(zero),X0,X1,X0) = f(s(s(zero)),s(zero),X1,X0),
inference(superposition,[status(thm)],[d7,d17]) ).
cnf(d19,plain,
f(s(s(X1)),zero,s(s(X0)),X2) = f(s(X1),X2,minus(X0,X1),X2),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d20,plain,
f(s(s(zero)),zero,s(s(X0)),X1) = f(s(zero),X1,X0,X1),
inference(superposition,[status(thm)],[c0,d19]) ).
cnf(d21,plain,
f(s(s(zero)),zero,s(s(X1)),X0) = f(s(s(zero)),s(zero),X1,X0),
inference(superposition,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
f(s(s(X0)),s(s(X1)),X2,X3) = if('\'<=\''(X0,X1),f(s(s(X0)),minus(s(X1),s(X0)),X2,X3),f(s(X0),X3,X2,X3)),
inference(superposition,[status(thm)],[c4,c12]) ).
cnf(d23,plain,
f(s(s(X1)),s(s(X0)),X2,X3) = if('\'<=\''(X1,X0),f(s(s(X1)),minus(X0,X1),X2,X3),f(s(X1),X3,X2,X3)),
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
f(s(s(zero)),s(s(X0)),X1,X2) = if(true,f(s(s(zero)),minus(X0,zero),X1,X2),f(s(zero),X2,X1,X2)),
inference(superposition,[status(thm)],[c2,d23]) ).
cnf(d25,plain,
f(s(s(zero)),s(s(X0)),X1,X2) = f(s(s(zero)),minus(X0,zero),X1,X2),
inference(demodulation,[status(thm)],[d24,c5]) ).
cnf(d26,plain,
f(s(s(zero)),s(s(X0)),X1,X2) = f(s(s(zero)),X0,X1,X2),
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
f(s(s(s(zero))),s(zero),X1,s(s(X0))) = f(s(s(zero)),X0,X1,s(s(X0))),
inference(superposition,[status(thm)],[d26,d7]) ).
cnf(d28,plain,
f(s(s(s(zero))),s(zero),X1,s(s(s(s(X0))))) = f(s(s(zero)),X0,X1,s(s(s(s(X0))))),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
f(s(s(s(zero))),s(zero),X1,s(s(s(s(s(s(X0))))))) = f(s(s(zero)),X0,X1,s(s(s(s(s(s(X0))))))),
inference(superposition,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
f(s(s(s(X1))),zero,s(s(s(X0))),X2) = f(s(s(X1)),X2,minus(X0,X1),X2),
inference(superposition,[status(thm)],[c1,d19]) ).
cnf(d31,plain,
f(s(s(s(zero))),zero,s(s(s(X0))),X1) = f(s(s(zero)),X1,X0,X1),
inference(superposition,[status(thm)],[c0,d30]) ).
cnf(d32,plain,
f(s(s(s(zero))),s(zero),X1,X0) = f(s(s(s(zero))),zero,s(s(s(X1))),X0),
inference(superposition,[status(thm)],[d31,d7]) ).
cnf(d33,plain,
f(s(s(X0)),s(X3),X2,X1) = if('\'<=\''(s(X0),X3),f(s(s(X0)),minus(X3,s(X0)),X2,X1),f(s(s(X0)),s(zero),X2,X1)),
inference(superposition,[status(thm)],[d7,c12]) ).
cnf(d34,plain,
f(s(s(X0)),s(X3),X1,X2) = if('\'<=\''(s(X0),X3),f(s(s(X0)),minus(X3,s(X0)),X1,X2),f(s(X0),X2,X1,X2)),
inference(superposition,[status(thm)],[d7,d33]) ).
cnf(d35,plain,
f(s(s(X0)),s(X1),X2,X3) = f(s(s(X0)),s(X1),X2,X3),
inference(demodulation,[status(thm)],[d34,c12]) ).
cnf(d36,plain,
f(s(s(s(X0))),s(s(s(X1))),X2,X3) = if('\'<=\''(X0,X1),f(s(s(s(X0))),minus(s(X1),s(X0)),X2,X3),f(s(s(X0)),X3,X2,X3)),
inference(superposition,[status(thm)],[c4,d23]) ).
cnf(d37,plain,
f(s(s(s(X1))),s(s(s(X0))),X2,X3) = if('\'<=\''(X1,X0),f(s(s(s(X1))),minus(X0,X1),X2,X3),f(s(s(X1)),X3,X2,X3)),
inference(demodulation,[status(thm)],[d36,c1]) ).
cnf(d38,plain,
f(s(s(s(zero))),s(s(s(X0))),X1,X2) = if(true,f(s(s(s(zero))),minus(X0,zero),X1,X2),f(s(s(zero)),X2,X1,X2)),
inference(superposition,[status(thm)],[c2,d37]) ).
cnf(d39,plain,
f(s(s(s(zero))),s(s(s(X0))),X1,X2) = f(s(s(s(zero))),minus(X0,zero),X1,X2),
inference(demodulation,[status(thm)],[d38,c5]) ).
cnf(d40,plain,
f(s(s(s(zero))),s(s(s(X0))),X1,X2) = f(s(s(s(zero))),X0,X1,X2),
inference(demodulation,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
f(s(s(s(zero))),X0,X1,X2) = f(s(s(s(zero))),s(s(s(X0))),X1,X2),
inference(superposition,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
f(s(s(s(s(zero)))),s(zero),X1,s(s(s(X0)))) = f(s(s(s(zero))),X0,X1,s(s(s(X0)))),
inference(superposition,[status(thm)],[d40,d7]) ).
cnf(d43,plain,
f(s(s(s(zero))),X0,X1,s(s(s(s(s(s(X0))))))) = f(s(s(s(s(zero)))),s(zero),X1,s(s(s(s(s(s(X0))))))),
inference(superposition,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
f(s(s(s(X0))),s(s(zero)),X1,X2) = if(false,f(s(s(s(X0))),minus(zero,s(X0)),X1,X2),f(s(s(X0)),X2,X1,X2)),
inference(superposition,[status(thm)],[c3,d23]) ).
cnf(d45,plain,
f(s(s(s(X0))),s(s(zero)),X1,X2) = f(s(s(X0)),X2,X1,X2),
inference(demodulation,[status(thm)],[d44,c6]) ).
cnf(d46,plain,
f(s(s(s(X0))),s(zero),X2,X1) = f(s(s(s(X0))),s(s(zero)),X2,X1),
inference(superposition,[status(thm)],[d45,d7]) ).
cnf(d47,plain,
f(s(s(s(s(X0)))),s(s(s(s(X1)))),X2,X3) = if('\'<=\''(X0,X1),f(s(s(s(s(X0)))),minus(s(X1),s(X0)),X2,X3),f(s(s(s(X0))),X3,X2,X3)),
inference(superposition,[status(thm)],[c4,d37]) ).
cnf(d48,plain,
f(s(s(s(s(X1)))),s(s(s(s(X0)))),X2,X3) = if('\'<=\''(X1,X0),f(s(s(s(s(X1)))),minus(X0,X1),X2,X3),f(s(s(s(X1))),X3,X2,X3)),
inference(demodulation,[status(thm)],[d47,c1]) ).
cnf(d49,plain,
f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = if(true,f(s(s(s(s(zero)))),minus(X0,zero),X1,X2),f(s(s(s(zero))),X2,X1,X2)),
inference(superposition,[status(thm)],[c2,d48]) ).
cnf(d50,plain,
f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(s(zero)))),minus(X0,zero),X1,X2),
inference(demodulation,[status(thm)],[d49,c5]) ).
cnf(d51,plain,
f(s(s(s(s(zero)))),s(s(s(s(X0)))),X1,X2) = f(s(s(s(s(zero)))),X0,X1,X2),
inference(demodulation,[status(thm)],[d50,c0]) ).
cnf(d52,plain,
f(s(s(s(s(s(zero))))),s(zero),X1,s(s(s(s(X0))))) = f(s(s(s(s(zero)))),X0,X1,s(s(s(s(X0))))),
inference(superposition,[status(thm)],[d51,d7]) ).
cnf(d53,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(s(s(zero)))),s(s(zero)),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))),
inference(superposition,[status(thm)],[d52,c8]) ).
cnf(d54,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(s(s(zero)))),s(zero),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d53,d46]) ).
cnf(d55,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(s(zero))),zero,s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d54,d43]) ).
cnf(d56,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(s(zero))),s(zero),s(s(s(zero))),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d55,d32]) ).
cnf(d57,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(zero)),zero,s(s(s(zero))),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d56,d29]) ).
cnf(d58,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(s(zero)),s(zero),s(zero),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d57,d21]) ).
cnf(d59,plain,
perfectp(s(s(s(s(s(s(zero))))))) = f(s(zero),zero,s(zero),s(s(s(s(s(s(zero))))))),
inference(demodulation,[status(thm)],[d58,d13]) ).
cnf(d60,plain,
perfectp(s(s(s(s(s(s(zero))))))) = true,
inference(demodulation,[status(thm)],[d59,d2]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[c13,d60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 04:32:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.34/6.25 % SZS status Unsatisfiable for theBenchmark.p
% 40.34/6.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------