%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN269-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:21:41 AM UTC 2026
% Result : Unsatisfiable 20.07s 18.19s
% Output : CNFRefutation 20.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of clauses : 88 ( 36 unt; 0 nHn; 68 RR)
% Number of literals : 166 ( 0 equ; 81 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 135 ( 46 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ p4(b,a,a) ).
cnf(axiom_1,axiom,
s0(d) ).
cnf(axiom_14,axiom,
p0(b,X0) ).
cnf(axiom_15,axiom,
n0(a,b) ).
cnf(axiom_17,axiom,
q0(X0,d) ).
cnf(axiom_19,axiom,
m0(X0,d,X1) ).
cnf(axiom_20,axiom,
l0(a) ).
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_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_136,axiom,
( ~ k1(b)
| m2(b) ) ).
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_188,axiom,
( ~ l0(X0)
| ~ r1(X0)
| r2(X0) ) ).
cnf(rule_192,axiom,
( ~ n0(X0,X3)
| ~ p2(X2,X1,X3)
| ~ s1(X1)
| k3(X0,X1,X0) ) ).
cnf(rule_210,axiom,
( ~ n2(X0)
| k3(X0,X0,X0) ) ).
cnf(rule_235,axiom,
( ~ k3(X0,X1,X0)
| ~ r2(X1)
| m3(X0,X0,X1) ) ).
cnf(rule_267,axiom,
( ~ p2(X0,X2,X1)
| r3(X0,X1,X0) ) ).
cnf(rule_268,axiom,
( ~ r3(X1,X3,X3)
| ~ m3(X2,b,X0)
| ~ m2(X1)
| r3(X0,X0,X1) ) ).
cnf(rule_287,axiom,
( ~ k3(X0,X0,X1)
| p4(X0,X1,X0) ) ).
cnf(rule_288,axiom,
( ~ p4(X2,X2,X3)
| ~ r3(X1,X1,X0)
| p4(X0,X1,X1) ) ).
cnf(c0,plain,
~ p4(b,a,a),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(c1,plain,
s0(d),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c14,plain,
p0(b,X0),
inference(clausification,[status(esa)],[axiom_14]) ).
cnf(c15,plain,
n0(a,b),
inference(clausification,[status(esa)],[axiom_15]) ).
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(c20,plain,
l0(a),
inference(clausification,[status(esa)],[axiom_20]) ).
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(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(c174,plain,
( ~ k1(b)
| m2(b) ),
inference(clausification,[status(esa)],[rule_136]) ).
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(c226,plain,
( ~ l0(X0)
| ~ r1(X0)
| r2(X0) ),
inference(clausification,[status(esa)],[rule_188]) ).
cnf(c230,plain,
( ~ n0(X0,X3)
| ~ p2(X2,X1,X3)
| ~ s1(X1)
| k3(X0,X1,X0) ),
inference(clausification,[status(esa)],[rule_192]) ).
cnf(c248,plain,
( ~ n2(X0)
| k3(X0,X0,X0) ),
inference(clausification,[status(esa)],[rule_210]) ).
cnf(c273,plain,
( ~ k3(X0,X1,X0)
| ~ r2(X1)
| m3(X0,X0,X1) ),
inference(clausification,[status(esa)],[rule_235]) ).
cnf(c305,plain,
( ~ p2(X0,X2,X1)
| r3(X0,X1,X0) ),
inference(clausification,[status(esa)],[rule_267]) ).
cnf(c306,plain,
( ~ r3(X1,X3,X3)
| ~ m3(X2,b,X0)
| ~ m2(X1)
| r3(X0,X0,X1) ),
inference(clausification,[status(esa)],[rule_268]) ).
cnf(c325,plain,
( ~ k3(X0,X0,X1)
| p4(X0,X1,X0) ),
inference(clausification,[status(esa)],[rule_287]) ).
cnf(c326,plain,
( ~ p4(X2,X2,X3)
| ~ r3(X1,X1,X0)
| p4(X0,X1,X1) ),
inference(clausification,[status(esa)],[rule_288]) ).
cnf(d0,plain,
p1(X0,X0,X0),
inference(resolution,[status(thm)],[c123,c14]) ).
cnf(d1,plain,
n2(X0),
inference(resolution,[status(thm)],[d0,c175]) ).
cnf(d2,plain,
k3(X0,X0,X0),
inference(resolution,[status(thm)],[d1,c248]) ).
cnf(d3,plain,
p4(X0,X0,X0),
inference(resolution,[status(thm)],[c325,d2]) ).
cnf(d4,plain,
s1(b),
inference(resolution,[status(thm)],[c163,c14]) ).
cnf(d5,plain,
( ~ s1(X1)
| s1(X0) ),
inference(resolution,[status(thm)],[c164,c17]) ).
cnf(d6,plain,
s1(X0),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( k3(X0,X3,X0)
| ~ p2(X2,X3,X1)
| ~ n0(X0,X1) ),
inference(resolution,[status(thm)],[d6,c230]) ).
cnf(d8,plain,
( q1(X2,X1,X2)
| ~ n0(X0,X1) ),
inference(resolution,[status(thm)],[c130,c14]) ).
cnf(d9,plain,
q1(X0,a,X0),
inference(resolution,[status(thm)],[d8,c37]) ).
cnf(d10,plain,
p2(X0,a,X0),
inference(resolution,[status(thm)],[d9,c179]) ).
cnf(d11,plain,
( k3(X0,a,X0)
| ~ n0(X0,X1) ),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
k3(b,a,b),
inference(resolution,[status(thm)],[d11,c37]) ).
cnf(d13,plain,
( m3(b,b,a)
| ~ r2(a) ),
inference(resolution,[status(thm)],[d12,c273]) ).
cnf(d14,plain,
q1(X0,X0,X0),
inference(resolution,[status(thm)],[c148,c19]) ).
cnf(d15,plain,
( r1(X0)
| ~ q1(d,X1,d)
| ~ q0(X0,X1) ),
inference(resolution,[status(thm)],[c1,c162]) ).
cnf(d16,plain,
( r1(X0)
| ~ q0(X0,d) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
r1(X0),
inference(resolution,[status(thm)],[c17,d16]) ).
cnf(d18,plain,
( r2(X0)
| ~ l0(X0) ),
inference(resolution,[status(thm)],[d17,c226]) ).
cnf(d19,plain,
r2(a),
inference(resolution,[status(thm)],[d18,c20]) ).
cnf(d20,plain,
m3(b,b,a),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
m1(X0,X0,X0),
inference(resolution,[status(thm)],[c44,c19]) ).
cnf(d22,plain,
p2(X0,X0,X0),
inference(resolution,[status(thm)],[c188,d21]) ).
cnf(d23,plain,
r3(X0,X0,X0),
inference(resolution,[status(thm)],[c305,d22]) ).
cnf(d24,plain,
( r3(X2,X2,X0)
| ~ m3(X1,b,X2)
| ~ m2(X0) ),
inference(resolution,[status(thm)],[c306,d23]) ).
cnf(d25,plain,
( r3(a,a,X0)
| ~ m2(X0) ),
inference(resolution,[status(thm)],[d24,d20]) ).
cnf(d26,plain,
( ~ p4(X1,X1,X2)
| p4(X0,a,a)
| ~ m2(X0) ),
inference(resolution,[status(thm)],[d25,c326]) ).
cnf(d27,plain,
( ~ m2(X0)
| p4(X0,a,a) ),
inference(resolution,[status(thm)],[d26,d3]) ).
cnf(d28,plain,
~ m2(b),
inference(resolution,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
k1(b),
inference(resolution,[status(thm)],[c39,c15]) ).
cnf(d30,plain,
m2(b),
inference(resolution,[status(thm)],[d29,c174]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN269-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n008.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Sat Sep 26 17:29:27 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.07/18.19 % SZS status Unsatisfiable for theBenchmark.p
% 20.07/18.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------