%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN143-10 : 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 09:21:24 AM UTC 2026
% Result : Unsatisfiable 50.85s 6.90s
% Output : CNFRefutation 50.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of clauses : 133 ( 133 unt; 0 nHn; 39 RR)
% Number of literals : 133 ( 132 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 172 ( 73 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(axiom_5,axiom,
s0(b) = true ).
cnf(axiom_11,axiom,
n0(e,b) = true ).
cnf(axiom_14,axiom,
p0(b,X0) = true ).
cnf(axiom_17,axiom,
q0(X0,d) = true ).
cnf(axiom_19,axiom,
m0(X0,d,X1) = true ).
cnf(axiom_20,axiom,
l0(a) = true ).
cnf(axiom_32,axiom,
k0(b) = true ).
cnf(axiom_34,axiom,
n0(c,d) = true ).
cnf(axiom_37,axiom,
n0(b,a) = true ).
cnf(rule_002,axiom,
ifeq(n0(X0,X1),true,l1(X1,X1),true) = true ).
cnf(rule_050,axiom,
ifeq(l0(X0),true,ifeq(p0(b,X1),true,ifeq(s0(b),true,n1(X0,X1,X0),true),true),true) = true ).
cnf(rule_054,axiom,
ifeq(n1(X0,X1,X0),true,ifeq(l0(X2),true,ifeq(l1(X2,X0),true,n1(X0,X1,X1),true),true),true) = true ).
cnf(rule_066,axiom,
ifeq(n0(X0,X1),true,p1(X1,X1,X1),true) = true ).
cnf(rule_075,axiom,
ifeq(p0(b,a),true,p1(a,a,a),true) = true ).
cnf(rule_085,axiom,
ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true ).
cnf(rule_125,axiom,
ifeq(p0(X0,X0),true,s1(X0),true) = true ).
cnf(rule_126,axiom,
ifeq(s1(X0),true,ifeq(q0(X1,X2),true,s1(X1),true),true) = true ).
cnf(rule_133,axiom,
ifeq(s1(X0),true,ifeq(p0(X1,X1),true,ifeq(m0(X2,X0,X3),true,l2(X3,X3),true),true),true) = true ).
cnf(rule_137,axiom,
ifeq(p1(X0,X1,X2),true,n2(X2),true) = true ).
cnf(rule_177,axiom,
ifeq(p1(X0,X0,X0),true,ifeq(k0(X1),true,q2(X0,X1,X1),true),true) = true ).
cnf(rule_181,axiom,
ifeq(p1(X0,X0,X0),true,q2(X0,X0,X0),true) = true ).
cnf(rule_182,axiom,
ifeq(q2(X0,X1,X2),true,ifeq(p1(X2,X2,X1),true,ifeq(n1(X0,X2,X1),true,q2(X2,X0,X2),true),true),true) = true ).
cnf(rule_189,axiom,
ifeq(q2(b,X0,b),true,ifeq(s1(b),true,s2(X0),true),true) = true ).
cnf(rule_244,axiom,
ifeq(n2(X0),true,p3(X0,X0,X0),true) = true ).
cnf(rule_273,axiom,
ifeq(s2(X0),true,ifeq(q2(X1,X0,X1),true,ifeq(m0(X1,X2,X3),true,s3(X0,X3),true),true),true) = true ).
cnf(rule_279,axiom,
ifeq(s3(a,X0),true,ifeq(l2(X1,X2),true,m4(X0,X2),true),true) = true ).
cnf(rule_299,axiom,
ifeq(p3(X0,X1,X2),true,ifeq(l1(X3,X1),true,s4(X3),true),true) = true ).
cnf(rule_305,axiom,
ifeq(s4(X0),true,ifeq(m4(e,e),true,m5(X0,X0),true),true) = true ).
cnf(prove_this,negated_conjecture,
m5(d,d) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c5,plain,
s0(b) = true,
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c11,plain,
n0(e,b) = true,
inference(clausification,[status(esa)],[axiom_11]) ).
cnf(c14,plain,
p0(b,X0) = true,
inference(clausification,[status(esa)],[axiom_14]) ).
cnf(c17,plain,
q0(X0,d) = true,
inference(clausification,[status(esa)],[axiom_17]) ).
cnf(c19,plain,
m0(X0,d,X1) = true,
inference(clausification,[status(esa)],[axiom_19]) ).
cnf(c20,plain,
l0(a) = true,
inference(clausification,[status(esa)],[axiom_20]) ).
cnf(c32,plain,
k0(b) = true,
inference(clausification,[status(esa)],[axiom_32]) ).
cnf(c34,plain,
n0(c,d) = true,
inference(clausification,[status(esa)],[axiom_34]) ).
cnf(c37,plain,
n0(b,a) = true,
inference(clausification,[status(esa)],[axiom_37]) ).
cnf(c40,plain,
ifeq(n0(X0,X1),true,l1(X1,X1),true) = true,
inference(clausification,[status(esa)],[rule_002]) ).
cnf(c87,plain,
ifeq(l0(X0),true,ifeq(p0(b,X1),true,ifeq(s0(b),true,n1(X0,X1,X0),true),true),true) = true,
inference(clausification,[status(esa)],[rule_050]) ).
cnf(c91,plain,
ifeq(n1(X0,X1,X0),true,ifeq(l0(X2),true,ifeq(l1(X2,X0),true,n1(X0,X1,X1),true),true),true) = true,
inference(clausification,[status(esa)],[rule_054]) ).
cnf(c103,plain,
ifeq(n0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(clausification,[status(esa)],[rule_066]) ).
cnf(c112,plain,
ifeq(p0(b,a),true,p1(a,a,a),true) = true,
inference(clausification,[status(esa)],[rule_075]) ).
cnf(c121,plain,
ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true,
inference(clausification,[status(esa)],[rule_085]) ).
cnf(c161,plain,
ifeq(p0(X0,X0),true,s1(X0),true) = true,
inference(clausification,[status(esa)],[rule_125]) ).
cnf(c162,plain,
ifeq(s1(X0),true,ifeq(q0(X1,X2),true,s1(X1),true),true) = true,
inference(clausification,[status(esa)],[rule_126]) ).
cnf(c168,plain,
ifeq(s1(X0),true,ifeq(p0(X1,X1),true,ifeq(m0(X2,X0,X3),true,l2(X3,X3),true),true),true) = true,
inference(clausification,[status(esa)],[rule_133]) ).
cnf(c172,plain,
ifeq(p1(X0,X1,X2),true,n2(X2),true) = true,
inference(clausification,[status(esa)],[rule_137]) ).
cnf(c212,plain,
ifeq(p1(X0,X0,X0),true,ifeq(k0(X1),true,q2(X0,X1,X1),true),true) = true,
inference(clausification,[status(esa)],[rule_177]) ).
cnf(c216,plain,
ifeq(p1(X0,X0,X0),true,q2(X0,X0,X0),true) = true,
inference(clausification,[status(esa)],[rule_181]) ).
cnf(c217,plain,
ifeq(q2(X0,X1,X2),true,ifeq(p1(X2,X2,X1),true,ifeq(n1(X0,X2,X1),true,q2(X2,X0,X2),true),true),true) = true,
inference(clausification,[status(esa)],[rule_182]) ).
cnf(c224,plain,
ifeq(q2(b,X0,b),true,ifeq(s1(b),true,s2(X0),true),true) = true,
inference(clausification,[status(esa)],[rule_189]) ).
cnf(c277,plain,
ifeq(n2(X0),true,p3(X0,X0,X0),true) = true,
inference(clausification,[status(esa)],[rule_244]) ).
cnf(c306,plain,
ifeq(s2(X0),true,ifeq(q2(X1,X0,X1),true,ifeq(m0(X1,X2,X3),true,s3(X0,X3),true),true),true) = true,
inference(clausification,[status(esa)],[rule_273]) ).
cnf(c311,plain,
ifeq(s3(a,X0),true,ifeq(l2(X1,X2),true,m4(X0,X2),true),true) = true,
inference(clausification,[status(esa)],[rule_279]) ).
cnf(c330,plain,
ifeq(p3(X0,X1,X2),true,ifeq(l1(X3,X1),true,s4(X3),true),true) = true,
inference(clausification,[status(esa)],[rule_299]) ).
cnf(c336,plain,
ifeq(s4(X0),true,ifeq(m4(e,e),true,m5(X0,X0),true),true) = true,
inference(clausification,[status(esa)],[rule_305]) ).
cnf(c362,plain,
m5(d,d) != true,
inference(clausification,[status(esa)],[prove_this]) ).
cnf(d0,plain,
ifeq(true,true,s1(b),true) = true,
inference(superposition,[status(thm)],[c14,c161]) ).
cnf(d1,plain,
s1(b) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(q2(b,X0,b),true,ifeq(true,true,s2(X0),true),true) = true,
inference(demodulation,[status(thm)],[c224,d1]) ).
cnf(d3,plain,
ifeq(q2(b,X0,b),true,s2(X0),true) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(true,true,p1(X0,X0,X0),true) = true,
inference(superposition,[status(thm)],[c14,c121]) ).
cnf(d5,plain,
p1(X0,X0,X0) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(p1(X0,X0,X0),true,ifeq(true,true,q2(X0,b,b),true),true) = true,
inference(superposition,[status(thm)],[c32,c212]) ).
cnf(d7,plain,
ifeq(true,true,ifeq(true,true,q2(X0,b,b),true),true) = true,
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
ifeq(true,true,q2(X0,b,b),true) = true,
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
q2(X0,b,b) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(true,true,p1(b,b,b),true) = true,
inference(superposition,[status(thm)],[c11,c103]) ).
cnf(d11,plain,
p1(b,b,b) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(q2(X0,b,b),true,ifeq(true,true,ifeq(n1(X0,b,b),true,q2(b,X0,b),true),true),true) = true,
inference(superposition,[status(thm)],[d11,c217]) ).
cnf(d13,plain,
ifeq(true,true,ifeq(true,true,ifeq(n1(X0,b,b),true,q2(b,X0,b),true),true),true) = true,
inference(demodulation,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
ifeq(true,true,ifeq(n1(X0,b,b),true,q2(b,X0,b),true),true) = true,
inference(demodulation,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
ifeq(n1(X0,b,b),true,q2(b,X0,b),true) = true,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
ifeq(l0(X1),true,ifeq(true,true,ifeq(s0(b),true,n1(X1,X0,X1),true),true),true) = true,
inference(demodulation,[status(thm)],[c87,c14]) ).
cnf(d17,plain,
ifeq(l0(X0),true,ifeq(s0(b),true,n1(X0,X1,X0),true),true) = true,
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
ifeq(l0(X0),true,ifeq(true,true,n1(X0,X1,X0),true),true) = true,
inference(demodulation,[status(thm)],[d17,c5]) ).
cnf(d19,plain,
ifeq(l0(X0),true,n1(X0,X1,X0),true) = true,
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
ifeq(true,true,n1(a,X0,a),true) = true,
inference(superposition,[status(thm)],[c20,d19]) ).
cnf(d21,plain,
n1(a,X0,a) = true,
inference(demodulation,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
ifeq(true,true,l1(a,a),true) = true,
inference(superposition,[status(thm)],[c37,c40]) ).
cnf(d23,plain,
l1(a,a) = true,
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
ifeq(n1(a,X0,a),true,ifeq(l0(a),true,ifeq(true,true,n1(a,X0,X0),true),true),true) = true,
inference(superposition,[status(thm)],[d23,c91]) ).
cnf(d25,plain,
ifeq(true,true,ifeq(l0(a),true,ifeq(true,true,n1(a,X0,X0),true),true),true) = true,
inference(demodulation,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
ifeq(l0(a),true,ifeq(true,true,n1(a,X0,X0),true),true) = true,
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
ifeq(true,true,ifeq(true,true,n1(a,X0,X0),true),true) = true,
inference(demodulation,[status(thm)],[d26,c20]) ).
cnf(d28,plain,
ifeq(true,true,n1(a,X0,X0),true) = true,
inference(demodulation,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
n1(a,X0,X0) = true,
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
ifeq(true,true,q2(b,a,b),true) = true,
inference(superposition,[status(thm)],[d29,d15]) ).
cnf(d31,plain,
q2(b,a,b) = true,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
ifeq(true,true,s2(a),true) = true,
inference(superposition,[status(thm)],[d31,d3]) ).
cnf(d33,plain,
s2(a) = true,
inference(demodulation,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
ifeq(true,true,p1(a,a,a),true) = true,
inference(demodulation,[status(thm)],[c112,c14]) ).
cnf(d35,plain,
p1(a,a,a) = true,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
ifeq(true,true,q2(a,a,a),true) = true,
inference(superposition,[status(thm)],[d35,c216]) ).
cnf(d37,plain,
q2(a,a,a) = true,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
ifeq(s2(a),true,ifeq(true,true,ifeq(m0(a,X0,X1),true,s3(a,X1),true),true),true) = true,
inference(superposition,[status(thm)],[d37,c306]) ).
cnf(d39,plain,
ifeq(true,true,ifeq(true,true,ifeq(m0(a,X0,X1),true,s3(a,X1),true),true),true) = true,
inference(demodulation,[status(thm)],[d38,d33]) ).
cnf(d40,plain,
ifeq(true,true,ifeq(m0(a,X0,X1),true,s3(a,X1),true),true) = true,
inference(demodulation,[status(thm)],[d39,c0]) ).
cnf(d41,plain,
ifeq(m0(a,X0,X1),true,s3(a,X1),true) = true,
inference(demodulation,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
ifeq(true,true,s3(a,X0),true) = true,
inference(superposition,[status(thm)],[c19,d41]) ).
cnf(d43,plain,
s3(a,X0) = true,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
ifeq(true,true,ifeq(q0(X0,X1),true,s1(X0),true),true) = true,
inference(superposition,[status(thm)],[d1,c162]) ).
cnf(d45,plain,
ifeq(q0(X0,X1),true,s1(X0),true) = true,
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
ifeq(true,true,s1(X0),true) = true,
inference(superposition,[status(thm)],[c17,d45]) ).
cnf(d47,plain,
s1(X0) = true,
inference(demodulation,[status(thm)],[d46,c0]) ).
cnf(d48,plain,
ifeq(s1(X0),true,ifeq(true,true,ifeq(m0(X1,X0,X2),true,l2(X2,X2),true),true),true) = true,
inference(superposition,[status(thm)],[c14,c168]) ).
cnf(d49,plain,
ifeq(true,true,ifeq(true,true,ifeq(m0(X1,X0,X2),true,l2(X2,X2),true),true),true) = true,
inference(demodulation,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
ifeq(true,true,ifeq(m0(X0,X1,X2),true,l2(X2,X2),true),true) = true,
inference(demodulation,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
ifeq(m0(X0,X1,X2),true,l2(X2,X2),true) = true,
inference(demodulation,[status(thm)],[d50,c0]) ).
cnf(d52,plain,
ifeq(true,true,l2(X1,X1),true) = true,
inference(superposition,[status(thm)],[c19,d51]) ).
cnf(d53,plain,
l2(X0,X0) = true,
inference(demodulation,[status(thm)],[d52,c0]) ).
cnf(d54,plain,
ifeq(s3(a,X1),true,ifeq(true,true,m4(X1,X0),true),true) = true,
inference(superposition,[status(thm)],[d53,c311]) ).
cnf(d55,plain,
ifeq(true,true,ifeq(true,true,m4(X0,X1),true),true) = true,
inference(demodulation,[status(thm)],[d54,d43]) ).
cnf(d56,plain,
ifeq(true,true,m4(X0,X1),true) = true,
inference(demodulation,[status(thm)],[d55,c0]) ).
cnf(d57,plain,
m4(X0,X1) = true,
inference(demodulation,[status(thm)],[d56,c0]) ).
cnf(d58,plain,
ifeq(true,true,l1(d,d),true) = true,
inference(superposition,[status(thm)],[c34,c40]) ).
cnf(d59,plain,
l1(d,d) = true,
inference(demodulation,[status(thm)],[d58,c0]) ).
cnf(d60,plain,
ifeq(p3(X0,d,X1),true,ifeq(true,true,s4(d),true),true) = true,
inference(superposition,[status(thm)],[d59,c330]) ).
cnf(d61,plain,
ifeq(p3(X0,d,X1),true,s4(d),true) = true,
inference(demodulation,[status(thm)],[d60,c0]) ).
cnf(d62,plain,
ifeq(true,true,n2(X0),true) = true,
inference(superposition,[status(thm)],[d5,c172]) ).
cnf(d63,plain,
n2(X0) = true,
inference(demodulation,[status(thm)],[d62,c0]) ).
cnf(d64,plain,
ifeq(true,true,p3(X0,X0,X0),true) = true,
inference(demodulation,[status(thm)],[c277,d63]) ).
cnf(d65,plain,
p3(X0,X0,X0) = true,
inference(demodulation,[status(thm)],[d64,c0]) ).
cnf(d66,plain,
ifeq(true,true,s4(d),true) = true,
inference(superposition,[status(thm)],[d65,d61]) ).
cnf(d67,plain,
s4(d) = true,
inference(demodulation,[status(thm)],[d66,c0]) ).
cnf(d68,plain,
ifeq(true,true,ifeq(m4(e,e),true,m5(d,d),true),true) = true,
inference(superposition,[status(thm)],[d67,c336]) ).
cnf(d69,plain,
ifeq(m4(e,e),true,m5(d,d),true) = true,
inference(demodulation,[status(thm)],[d68,c0]) ).
cnf(d70,plain,
ifeq(true,true,m5(d,d),true) = true,
inference(demodulation,[status(thm)],[d69,d57]) ).
cnf(d71,plain,
m5(d,d) = true,
inference(demodulation,[status(thm)],[d70,c0]) ).
cnf(d72,plain,
$false,
inference(resolution,[status(thm)],[c362,d71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN143-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:18:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.85/6.90 % SZS status Unsatisfiable for theBenchmark.p
% 50.85/6.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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