%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 09:21:12 AM UTC 2026
% Result : Unsatisfiable 12.75s 2.09s
% Output : CNFRefutation 12.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of clauses : 47 ( 10 unt; 13 nHn; 47 RR)
% Number of literals : 135 ( 0 equ; 81 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
( 'big$uk'(X1)
| ~ 'big$uh'(X0,X1)
| ~ 'big$ug'(X1)
| 'big$ug'(f(X0))
| ~ 'big$uf'(X0) ) ).
cnf(clause_2,axiom,
( 'big$uk'(X1)
| ~ 'big$uh'(X0,X1)
| ~ 'big$ug'(X1)
| 'big$uh'(X0,f(X0))
| ~ 'big$uf'(X0) ) ).
cnf(clause_3,axiom,
( 'big$uk'(X1)
| ~ 'big$uh'(X0,X1)
| ~ 'big$ug'(X1)
| ~ 'big$uj'(X0,f(X0))
| ~ 'big$uf'(X0) ) ).
cnf(clause_4,axiom,
( ~ 'big$uk'(X0)
| ~ 'big$ul'(X0) ) ).
cnf(clause_5,axiom,
'big$uf'(a) ).
cnf(clause_6,axiom,
( 'big$ul'(X0)
| ~ 'big$uh'(a,X0) ) ).
cnf(clause_7,axiom,
( 'big$uj'(a,X0)
| ~ 'big$uh'(a,X0)
| ~ 'big$ug'(X0) ) ).
cnf(clause_8,negated_conjecture,
( 'big$ug'(g(X0))
| ~ 'big$uf'(X0) ) ).
cnf(clause_9,negated_conjecture,
( 'big$uh'(X0,g(X0))
| ~ 'big$uf'(X0) ) ).
cnf(c0,plain,
( 'big$uk'(X1)
| 'big$ug'(f(X0))
| ~ 'big$uh'(X0,X1)
| ~ 'big$ug'(X1)
| ~ 'big$uf'(X0) ),
inference(clausification,[status(esa)],[clause_1]) ).
cnf(c1,plain,
( 'big$uh'(X0,f(X0))
| ~ 'big$ug'(X1)
| 'big$uk'(X1)
| ~ 'big$uh'(X0,X1)
| ~ 'big$uf'(X0) ),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c2,plain,
( ~ 'big$uh'(X0,X1)
| ~ 'big$ug'(X1)
| 'big$uk'(X1)
| ~ 'big$uj'(X0,f(X0))
| ~ 'big$uf'(X0) ),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c3,plain,
( ~ 'big$uk'(X0)
| ~ 'big$ul'(X0) ),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
'big$uf'(a),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c5,plain,
( 'big$ul'(X0)
| ~ 'big$uh'(a,X0) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c6,plain,
( 'big$uj'(a,X0)
| ~ 'big$uh'(a,X0)
| ~ 'big$ug'(X0) ),
inference(clausification,[status(esa)],[clause_7]) ).
cnf(c7,plain,
( 'big$ug'(g(X0))
| ~ 'big$uf'(X0) ),
inference(clausification,[status(esa)],[clause_8]) ).
cnf(c8,plain,
( 'big$uh'(X0,g(X0))
| ~ 'big$uf'(X0) ),
inference(clausification,[status(esa)],[clause_9]) ).
cnf(d0,plain,
( 'big$uk'(g(X0))
| ~ 'big$ug'(g(X0))
| 'big$uh'(X0,f(X0))
| ~ 'big$uf'(X0)
| ~ 'big$uf'(X0) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d1,plain,
( 'big$uj'(a,f(a))
| ~ 'big$ug'(f(a))
| 'big$uk'(g(a))
| ~ 'big$ug'(g(a))
| ~ 'big$uf'(a) ),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( 'big$uj'(a,f(a))
| 'big$uk'(g(a))
| ~ 'big$ug'(g(a))
| ~ 'big$ug'(f(a)) ),
inference(resolution,[status(thm)],[c4,d1]) ).
cnf(d3,plain,
( 'big$ul'(g(a))
| ~ 'big$uf'(a) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(d4,plain,
'big$ul'(g(a)),
inference(resolution,[status(thm)],[c4,d3]) ).
cnf(d5,plain,
~ 'big$uk'(g(a)),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( 'big$uj'(a,f(a))
| ~ 'big$ug'(g(a))
| ~ 'big$ug'(f(a)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( 'big$uk'(g(X0))
| 'big$ug'(f(X0))
| ~ 'big$ug'(g(X0))
| ~ 'big$uf'(X0)
| ~ 'big$uf'(X0) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d8,plain,
( ~ 'big$uf'(X0)
| 'big$uk'(g(X0))
| 'big$ug'(f(X0))
| ~ 'big$uf'(X0) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d9,plain,
( 'big$ug'(f(a))
| ~ 'big$uf'(a) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
'big$ug'(f(a)),
inference(resolution,[status(thm)],[c4,d9]) ).
cnf(d11,plain,
( 'big$uj'(a,f(a))
| ~ 'big$ug'(g(a)) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( 'big$uk'(X0)
| ~ 'big$ug'(X0)
| ~ 'big$uh'(a,X0)
| ~ 'big$uf'(a)
| ~ 'big$ug'(g(a)) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( 'big$uk'(X0)
| ~ 'big$ug'(g(a))
| ~ 'big$ug'(X0)
| ~ 'big$uh'(a,X0) ),
inference(resolution,[status(thm)],[c4,d12]) ).
cnf(d14,plain,
( ~ 'big$uf'(a)
| 'big$uk'(X0)
| ~ 'big$ug'(X0)
| ~ 'big$uh'(a,X0) ),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
( 'big$uk'(X0)
| ~ 'big$ug'(X0)
| ~ 'big$uh'(a,X0) ),
inference(resolution,[status(thm)],[c4,d14]) ).
cnf(d16,plain,
( 'big$uk'(g(a))
| ~ 'big$ug'(g(a))
| ~ 'big$uf'(a)
| 'big$uk'(f(a))
| ~ 'big$ug'(f(a)) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( 'big$uk'(g(a))
| 'big$uk'(f(a))
| ~ 'big$ug'(g(a))
| ~ 'big$ug'(f(a)) ),
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
( 'big$uk'(f(a))
| ~ 'big$ug'(g(a))
| ~ 'big$ug'(f(a)) ),
inference(resolution,[status(thm)],[d5,d17]) ).
cnf(d19,plain,
( 'big$uk'(f(a))
| ~ 'big$ug'(g(a)) ),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
( 'big$ul'(f(a))
| 'big$uk'(g(a))
| ~ 'big$ug'(g(a))
| ~ 'big$uf'(a) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d21,plain,
( 'big$ul'(f(a))
| 'big$uk'(g(a))
| ~ 'big$ug'(g(a)) ),
inference(resolution,[status(thm)],[c4,d20]) ).
cnf(d22,plain,
( 'big$ul'(f(a))
| ~ 'big$ug'(g(a)) ),
inference(resolution,[status(thm)],[d5,d21]) ).
cnf(d23,plain,
( ~ 'big$uf'(a)
| 'big$ul'(f(a)) ),
inference(resolution,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
'big$ul'(f(a)),
inference(resolution,[status(thm)],[c4,d23]) ).
cnf(d25,plain,
~ 'big$uk'(f(a)),
inference(resolution,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
~ 'big$ug'(g(a)),
inference(resolution,[status(thm)],[d25,d19]) ).
cnf(d27,plain,
~ 'big$uf'(a),
inference(resolution,[status(thm)],[d26,c7]) ).
cnf(d28,plain,
$false,
inference(resolution,[status(thm)],[c4,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:09:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.75/2.09 % SZS status Unsatisfiable for theBenchmark.p
% 12.75/2.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------