%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 09:21:55 AM UTC 2026
% Result : Unsatisfiable 7.38s 1.93s
% Output : CNFRefutation 7.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 11
% Syntax : Number of clauses : 60 ( 4 unt; 42 nHn; 38 RR)
% Number of literals : 186 ( 0 equ; 68 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 131 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause1,negated_conjecture,
( f(X2,X0,X1)
| f(X1,X2,X0)
| ~ f(a,a,z(X0,X1,X2))
| ~ f(X0,X1,X2) ) ).
cnf(clause2,negated_conjecture,
( ~ f(X2,X1,z(X1,X2,X0))
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ) ).
cnf(clause3,negated_conjecture,
( ~ f(X2,X1,z(X1,X2,X0))
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ) ).
cnf(clause4,negated_conjecture,
( f(X2,X1,z(X1,X2,X0))
| f(X0,X1,X2) ) ).
cnf(clause6,negated_conjecture,
( ~ f(X2,z(X2,X0,X1),X0)
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ) ).
cnf(clause7,negated_conjecture,
( ~ f(X2,z(X2,X0,X1),X0)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ) ).
cnf(clause8,negated_conjecture,
( f(X2,z(X2,X0,X1),X0)
| f(X0,X1,X2) ) ).
cnf(clause10,negated_conjecture,
( ~ f(z(X1,X2,X0),X2,X1)
| f(X1,X2,X0)
| f(X0,X1,X2) ) ).
cnf(clause11,negated_conjecture,
( ~ f(z(X2,X0,X1),X0,X2)
| f(X2,X0,X1)
| f(X0,X1,X2) ) ).
cnf(clause12,negated_conjecture,
( f(z(X1,X2,X0),X2,X1)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ) ).
cnf(clause17,negated_conjecture,
( ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2))
| ~ f(X2,X0,X1)
| ~ f(X1,X2,X0)
| ~ f(X0,X1,X2) ) ).
cnf(c0,plain,
( f(X2,X0,X1)
| f(X1,X2,X0)
| ~ f(a,a,z(X0,X1,X2))
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause1]) ).
cnf(c1,plain,
( ~ f(X2,X1,z(X1,X2,X0))
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause2]) ).
cnf(c2,plain,
( ~ f(X2,X1,z(X1,X2,X0))
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause3]) ).
cnf(c3,plain,
( f(X2,X1,z(X1,X2,X0))
| f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause4]) ).
cnf(c5,plain,
( ~ f(X2,z(X2,X0,X1),X0)
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause6]) ).
cnf(c6,plain,
( ~ f(X2,z(X2,X0,X1),X0)
| f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause7]) ).
cnf(c7,plain,
( f(X2,z(X2,X0,X1),X0)
| f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause8]) ).
cnf(c9,plain,
( ~ f(z(X1,X2,X0),X2,X1)
| f(X1,X2,X0)
| f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause10]) ).
cnf(c10,plain,
( ~ f(z(X2,X0,X1),X0,X2)
| f(X2,X0,X1)
| f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause11]) ).
cnf(c11,plain,
( f(z(X1,X2,X0),X2,X1)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause12]) ).
cnf(c16,plain,
( ~ f(z(X0,X1,X2),z(X0,X1,X2),z(X0,X1,X2))
| ~ f(X2,X0,X1)
| ~ f(X1,X2,X0)
| ~ f(X0,X1,X2) ),
inference(clausification,[status(esa)],[clause17]) ).
cnf(d0,plain,
( ~ f(a,a,X0)
| f(a,X0,a)
| f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
( f(X0,a,a)
| f(a,z(a,a,X0),a)
| f(z(a,a,X0),a,a) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( f(a,a,X0)
| f(X0,a,a)
| f(a,z(a,a,X0),a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( ~ f(a,X0,a)
| f(X0,a,a)
| f(a,a,X0)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( f(a,X0,a)
| f(a,a,z(a,a,X0))
| f(z(a,a,X0),a,a) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( f(a,a,X0)
| f(a,X0,a)
| f(a,a,z(a,a,X0))
| f(a,X0,a) ),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( f(a,a,X0)
| ~ f(X0,a,a)
| f(a,a,X0)
| f(a,X0,a) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( ~ f(X0,a,a)
| ~ f(a,X0,a)
| f(a,a,z(a,a,X0))
| f(a,z(a,a,X0),a) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
( ~ f(a,X0,a)
| f(a,a,X0)
| f(a,a,z(a,a,X0))
| ~ f(a,X0,a)
| ~ f(X0,a,a) ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
( f(a,a,X0)
| ~ f(X0,a,a)
| f(a,a,X0)
| ~ f(a,X0,a)
| ~ f(X0,a,a) ),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
( f(a,X0,a)
| f(a,a,z(a,a,X0))
| ~ f(z(a,a,X0),a,a) ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
( f(a,a,z(a,a,X0))
| f(a,X0,a)
| f(a,a,z(a,a,X0))
| f(a,X0,a) ),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
( f(a,X0,a)
| ~ f(X0,a,a)
| f(a,X0,a) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( f(a,z(a,a,X0),a)
| f(X0,a,a)
| f(a,z(a,a,X0),a) ),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( ~ f(a,X0,a)
| f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( f(X0,a,a)
| f(z(a,a,X0),a,a) ),
inference(resolution,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
( f(a,a,X0)
| f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( f(a,X0,a)
| f(a,a,X0) ),
inference(resolution,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
( f(a,a,X0)
| ~ f(X0,a,a)
| f(a,a,X0) ),
inference(resolution,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
( f(a,X0,a)
| f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d16,d0]) ).
cnf(d20,plain,
( f(X0,a,a)
| f(X0,a,a) ),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
f(a,a,X0),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( ~ f(X1,X2,X0)
| f(X2,X0,X1)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
( f(X2,X0,X1)
| f(z(X0,X1,X2),X1,X0)
| f(X0,z(X0,X1,X2),X1) ),
inference(resolution,[status(thm)],[d22,c3]) ).
cnf(d24,plain,
( f(X1,X2,X0)
| f(X0,X1,X2)
| f(X1,z(X1,X2,X0),X2)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d23,c9]) ).
cnf(d25,plain,
( ~ f(X2,X1,X0)
| ~ f(X0,X2,X1)
| f(X1,z(X1,X0,X2),X0)
| f(X0,X1,z(X1,X0,X2)) ),
inference(resolution,[status(thm)],[d22,c11]) ).
cnf(d26,plain,
( ~ f(X2,X0,X1)
| f(X1,X2,X0)
| f(X2,X1,z(X1,X2,X0))
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
( f(X2,X0,X1)
| ~ f(X1,X2,X0)
| ~ f(X1,X2,X0)
| f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d26,c1]) ).
cnf(d28,plain,
( f(X2,X0,X1)
| ~ f(X0,z(X0,X1,X2),X1)
| f(z(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[d27,c3]) ).
cnf(d29,plain,
( f(X0,X1,X2)
| f(X1,X2,X0)
| f(z(X1,X2,X0),X2,X1)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
( f(X0,X1,X2)
| f(X2,X0,X1)
| f(X2,X0,X1)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d29,c9]) ).
cnf(d31,plain,
( ~ f(X2,X0,X1)
| f(X0,X1,X2)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
( f(X0,X1,X2)
| f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
f(X0,X0,X0),
inference(factoring,[status(thm)],[d30]) ).
cnf(d34,plain,
( ~ f(X1,X2,X0)
| ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d33,c16]) ).
cnf(d35,plain,
( ~ f(X2,X0,X1)
| ~ f(X0,X1,X2) ),
inference(resolution,[status(thm)],[d32,d34]) ).
cnf(d36,plain,
~ f(X0,X1,X2),
inference(resolution,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[d32,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:35:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.38/1.93 % SZS status Unsatisfiable for theBenchmark.p
% 7.38/1.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------