%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN156-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:21:26 AM UTC 2026
% Result : Unsatisfiable 21.63s 3.23s
% Output : CNFRefutation 21.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of clauses : 113 ( 46 unt; 0 nHn; 90 RR)
% Number of literals : 221 ( 0 equ; 111 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 24 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 156 ( 57 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ n4(a,e) ).
cnf(axiom_1,axiom,
s0(d) ).
cnf(axiom_11,axiom,
n0(e,b) ).
cnf(axiom_14,axiom,
p0(b,X0) ).
cnf(axiom_17,axiom,
q0(X0,d) ).
cnf(axiom_19,axiom,
m0(X0,d,X1) ).
cnf(axiom_28,axiom,
k0(e) ).
cnf(axiom_31,axiom,
m0(b,b,e) ).
cnf(axiom_32,axiom,
k0(b) ).
cnf(axiom_34,axiom,
n0(c,d) ).
cnf(axiom_37,axiom,
n0(b,a) ).
cnf(rule_001,axiom,
( ~ n0(X1,X0)
| k1(X0) ) ).
cnf(rule_006,axiom,
( ~ m0(X1,X1,X0)
| m1(X0,X0,X0) ) ).
cnf(rule_036,axiom,
( ~ m0(b,X1,X0)
| n1(X0,X0,X1) ) ).
cnf(rule_085,axiom,
( ~ p0(X1,X0)
| p1(X0,X0,X0) ) ).
cnf(rule_092,axiom,
( ~ p0(X3,X0)
| ~ n0(X2,X1)
| q1(X0,X1,X0) ) ).
cnf(rule_110,axiom,
( ~ m0(X1,X2,X0)
| q1(X0,X0,X0) ) ).
cnf(rule_124,axiom,
( ~ q1(d,X1,d)
| ~ s0(d)
| ~ q0(X0,X1)
| r1(X0) ) ).
cnf(rule_125,axiom,
( ~ p0(X0,X0)
| s1(X0) ) ).
cnf(rule_126,axiom,
( ~ s1(X2)
| ~ q0(X0,X1)
| s1(X0) ) ).
cnf(rule_137,axiom,
( ~ p1(X1,X2,X0)
| n2(X0) ) ).
cnf(rule_141,axiom,
( ~ q1(X0,a,X0)
| p2(X0,a,X0) ) ).
cnf(rule_150,axiom,
( ~ m1(X1,X1,X0)
| p2(X0,X0,X0) ) ).
cnf(rule_155,axiom,
( ~ p2(e,X0,X1)
| ~ k1(X2)
| p2(X0,X1,X1) ) ).
cnf(rule_181,axiom,
( ~ p1(X0,X0,X0)
| q2(X0,X0,X0) ) ).
cnf(rule_187,axiom,
( ~ q2(X1,X1,X1)
| ~ k0(X1)
| ~ m0(X2,X3,X0)
| ~ r1(X1)
| q2(X0,X1,X0) ) ).
cnf(rule_189,axiom,
( ~ s1(b)
| ~ q2(b,X0,b)
| s2(X0) ) ).
cnf(rule_236,axiom,
( ~ n2(X0)
| m3(X0,X0,X0) ) ).
cnf(rule_240,axiom,
( ~ p2(X1,X2,X0)
| n3(X0) ) ).
cnf(rule_251,axiom,
( ~ p2(X0,X1,X3)
| ~ m3(X1,X2,X3)
| p3(X0,X1,X1) ) ).
cnf(rule_255,axiom,
( ~ n0(X2,X0)
| ~ q2(X2,X0,X1)
| q3(X0,X1) ) ).
cnf(rule_257,axiom,
( ~ q3(X1,X0)
| ~ s2(X0)
| ~ n1(X2,X0,X1)
| q3(X0,X1) ) ).
cnf(rule_274,axiom,
( ~ n3(e)
| ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ) ).
cnf(rule_281,axiom,
( ~ n4(X0,X0)
| ~ p3(X0,X1,X1)
| n4(X0,X1) ) ).
cnf(rule_284,axiom,
( ~ m3(X0,X0,X0)
| ~ k4(X1)
| n4(X0,X0) ) ).
cnf(c0,plain,
~ n4(a,e),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(c1,plain,
s0(d),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c11,plain,
n0(e,b),
inference(clausification,[status(esa)],[axiom_11]) ).
cnf(c14,plain,
p0(b,X0),
inference(clausification,[status(esa)],[axiom_14]) ).
cnf(c17,plain,
q0(X0,d),
inference(clausification,[status(esa)],[axiom_17]) ).
cnf(c19,plain,
m0(X0,d,X1),
inference(clausification,[status(esa)],[axiom_19]) ).
cnf(c28,plain,
k0(e),
inference(clausification,[status(esa)],[axiom_28]) ).
cnf(c31,plain,
m0(b,b,e),
inference(clausification,[status(esa)],[axiom_31]) ).
cnf(c32,plain,
k0(b),
inference(clausification,[status(esa)],[axiom_32]) ).
cnf(c34,plain,
n0(c,d),
inference(clausification,[status(esa)],[axiom_34]) ).
cnf(c37,plain,
n0(b,a),
inference(clausification,[status(esa)],[axiom_37]) ).
cnf(c39,plain,
( ~ n0(X1,X0)
| k1(X0) ),
inference(clausification,[status(esa)],[rule_001]) ).
cnf(c44,plain,
( ~ m0(X1,X1,X0)
| m1(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_006]) ).
cnf(c74,plain,
( ~ m0(b,X1,X0)
| n1(X0,X0,X1) ),
inference(clausification,[status(esa)],[rule_036]) ).
cnf(c123,plain,
( ~ p0(X1,X0)
| p1(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_085]) ).
cnf(c130,plain,
( ~ p0(X3,X0)
| ~ n0(X2,X1)
| q1(X0,X1,X0) ),
inference(clausification,[status(esa)],[rule_092]) ).
cnf(c148,plain,
( ~ m0(X1,X2,X0)
| q1(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_110]) ).
cnf(c162,plain,
( ~ q1(d,X1,d)
| ~ s0(d)
| ~ q0(X0,X1)
| r1(X0) ),
inference(clausification,[status(esa)],[rule_124]) ).
cnf(c163,plain,
( ~ p0(X0,X0)
| s1(X0) ),
inference(clausification,[status(esa)],[rule_125]) ).
cnf(c164,plain,
( ~ s1(X2)
| ~ q0(X0,X1)
| s1(X0) ),
inference(clausification,[status(esa)],[rule_126]) ).
cnf(c175,plain,
( ~ p1(X1,X2,X0)
| n2(X0) ),
inference(clausification,[status(esa)],[rule_137]) ).
cnf(c179,plain,
( ~ q1(X0,a,X0)
| p2(X0,a,X0) ),
inference(clausification,[status(esa)],[rule_141]) ).
cnf(c188,plain,
( ~ m1(X1,X1,X0)
| p2(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_150]) ).
cnf(c193,plain,
( ~ p2(e,X0,X1)
| ~ k1(X2)
| p2(X0,X1,X1) ),
inference(clausification,[status(esa)],[rule_155]) ).
cnf(c219,plain,
( ~ p1(X0,X0,X0)
| q2(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_181]) ).
cnf(c225,plain,
( q2(X3,X0,X3)
| ~ m0(X1,X2,X3)
| ~ q2(X0,X0,X0)
| ~ r1(X0)
| ~ k0(X0) ),
inference(clausification,[status(esa)],[rule_187]) ).
cnf(c227,plain,
( ~ s1(b)
| ~ q2(b,X0,b)
| s2(X0) ),
inference(clausification,[status(esa)],[rule_189]) ).
cnf(c274,plain,
( ~ n2(X0)
| m3(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_236]) ).
cnf(c278,plain,
( ~ p2(X1,X2,X0)
| n3(X0) ),
inference(clausification,[status(esa)],[rule_240]) ).
cnf(c289,plain,
( ~ p2(X0,X1,X3)
| ~ m3(X1,X2,X3)
| p3(X0,X1,X1) ),
inference(clausification,[status(esa)],[rule_251]) ).
cnf(c293,plain,
( ~ n0(X2,X0)
| ~ q2(X2,X0,X1)
| q3(X0,X1) ),
inference(clausification,[status(esa)],[rule_255]) ).
cnf(c295,plain,
( ~ q3(X1,X0)
| ~ s2(X0)
| ~ n1(X2,X0,X1)
| q3(X0,X1) ),
inference(clausification,[status(esa)],[rule_257]) ).
cnf(c312,plain,
( ~ n3(e)
| ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ),
inference(clausification,[status(esa)],[rule_274]) ).
cnf(c319,plain,
( ~ n4(X0,X0)
| ~ p3(X0,X1,X1)
| n4(X0,X1) ),
inference(clausification,[status(esa)],[rule_281]) ).
cnf(c322,plain,
( ~ m3(X0,X0,X0)
| ~ k4(X1)
| n4(X0,X0) ),
inference(clausification,[status(esa)],[rule_284]) ).
cnf(d0,plain,
k1(a),
inference(resolution,[status(thm)],[c39,c37]) ).
cnf(d1,plain,
( q1(X2,X1,X2)
| ~ n0(X0,X1) ),
inference(resolution,[status(thm)],[c130,c14]) ).
cnf(d2,plain,
q1(X0,a,X0),
inference(resolution,[status(thm)],[d1,c37]) ).
cnf(d3,plain,
p2(X0,a,X0),
inference(resolution,[status(thm)],[d2,c179]) ).
cnf(d4,plain,
( p2(a,e,e)
| ~ k1(X0) ),
inference(resolution,[status(thm)],[d3,c193]) ).
cnf(d5,plain,
p2(a,e,e),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
p1(X0,X0,X0),
inference(resolution,[status(thm)],[c123,c14]) ).
cnf(d7,plain,
n2(X0),
inference(resolution,[status(thm)],[d6,c175]) ).
cnf(d8,plain,
m3(X0,X0,X0),
inference(resolution,[status(thm)],[d7,c274]) ).
cnf(d9,plain,
( p3(X0,X1,X1)
| ~ p2(X0,X1,X1) ),
inference(resolution,[status(thm)],[c289,d8]) ).
cnf(d10,plain,
p3(a,e,e),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( ~ n4(a,a)
| n4(a,e) ),
inference(resolution,[status(thm)],[d10,c319]) ).
cnf(d12,plain,
~ n4(a,a),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( ~ k4(X1)
| n4(X0,X0) ),
inference(resolution,[status(thm)],[d8,c322]) ).
cnf(d14,plain,
( k4(c)
| ~ q3(e,b)
| ~ n3(e) ),
inference(resolution,[status(thm)],[c34,c312]) ).
cnf(d15,plain,
m1(X0,X0,X0),
inference(resolution,[status(thm)],[c44,c19]) ).
cnf(d16,plain,
p2(X0,X0,X0),
inference(resolution,[status(thm)],[c188,d15]) ).
cnf(d17,plain,
n3(X0),
inference(resolution,[status(thm)],[c278,d16]) ).
cnf(d18,plain,
( k4(c)
| ~ q3(e,b) ),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
n1(e,e,b),
inference(resolution,[status(thm)],[c74,c31]) ).
cnf(d20,plain,
( q3(e,b)
| ~ q3(b,e)
| ~ s2(e) ),
inference(resolution,[status(thm)],[c295,d19]) ).
cnf(d21,plain,
s1(b),
inference(resolution,[status(thm)],[c163,c14]) ).
cnf(d22,plain,
( ~ s1(X1)
| s1(X0) ),
inference(resolution,[status(thm)],[c164,c17]) ).
cnf(d23,plain,
s1(X0),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( s2(X0)
| ~ q2(b,X0,b) ),
inference(resolution,[status(thm)],[d23,c227]) ).
cnf(d25,plain,
q1(X0,X0,X0),
inference(resolution,[status(thm)],[c148,c19]) ).
cnf(d26,plain,
( r1(X0)
| ~ q1(d,X1,d)
| ~ q0(X0,X1) ),
inference(resolution,[status(thm)],[c1,c162]) ).
cnf(d27,plain,
( r1(X0)
| ~ q0(X0,d) ),
inference(resolution,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
r1(X0),
inference(resolution,[status(thm)],[c17,d27]) ).
cnf(d29,plain,
( ~ q2(X3,X3,X3)
| q2(X2,X3,X2)
| ~ k0(X3)
| ~ m0(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,c225]) ).
cnf(d30,plain,
q2(X0,X0,X0),
inference(resolution,[status(thm)],[d6,c219]) ).
cnf(d31,plain,
( q2(X2,X3,X2)
| ~ k0(X3)
| ~ m0(X0,X1,X2) ),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( q2(X1,X0,X1)
| ~ k0(X0) ),
inference(resolution,[status(thm)],[d31,c19]) ).
cnf(d33,plain,
( s2(X0)
| ~ k0(X0) ),
inference(resolution,[status(thm)],[d32,d24]) ).
cnf(d34,plain,
s2(e),
inference(resolution,[status(thm)],[d33,c28]) ).
cnf(d35,plain,
( ~ q3(b,e)
| q3(e,b) ),
inference(resolution,[status(thm)],[d34,d20]) ).
cnf(d36,plain,
( q3(X0,X1)
| ~ n0(X1,X0)
| ~ k0(X0) ),
inference(resolution,[status(thm)],[d32,c293]) ).
cnf(d37,plain,
( q3(b,e)
| ~ k0(b) ),
inference(resolution,[status(thm)],[d36,c11]) ).
cnf(d38,plain,
q3(b,e),
inference(resolution,[status(thm)],[c32,d37]) ).
cnf(d39,plain,
q3(e,b),
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
k4(c),
inference(resolution,[status(thm)],[d39,d18]) ).
cnf(d41,plain,
n4(X0,X0),
inference(resolution,[status(thm)],[d40,d13]) ).
cnf(d42,plain,
$false,
inference(resolution,[status(thm)],[d41,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN156-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:17:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.63/3.23 % SZS status Unsatisfiable for theBenchmark.p
% 21.63/3.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------