%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN077-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 09:21:14 AM UTC 2026
% Result : Unsatisfiable 11.18s 2.99s
% Output : CNFRefutation 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of clauses : 29 ( 4 unt; 10 nHn; 26 RR)
% Number of literals : 82 ( 7 equ; 49 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
( X0 = X1
| ~ 'big$uf'(X0,f(X1)) ) ).
cnf(clause_2,axiom,
( 'big$uf'(X0,f(X1))
| X0 != X1 ) ).
cnf(clause_3,negated_conjecture,
( 'big$uf'(g(X0,X1),X1)
| ~ 'big$uf'(X0,X1)
| ~ 'big$uf'(X0,a) ) ).
cnf(clause_4,negated_conjecture,
( ~ 'big$uf'(X2,X1)
| ~ 'big$uf'(X2,g(X0,X1))
| ~ 'big$uf'(X0,X1)
| ~ 'big$uf'(X0,a) ) ).
cnf(clause_5,negated_conjecture,
( 'big$uf'(X0,a)
| 'big$uf'(X0,h(X0)) ) ).
cnf(clause_6,negated_conjecture,
( 'big$uf'(X1,a)
| 'big$uf'(i(X1,X0),X0)
| ~ 'big$uf'(X0,h(X1)) ) ).
cnf(clause_7,negated_conjecture,
( ~ 'big$uf'(X1,h(X0))
| 'big$uf'(i(X0,X1),h(X0))
| 'big$uf'(X0,a) ) ).
cnf(c0,plain,
( X0 = X1
| ~ 'big$uf'(X0,f(X1)) ),
inference(clausification,[status(esa)],[clause_1]) ).
cnf(c1,plain,
( 'big$uf'(X0,f(X1))
| X0 != X1 ),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c2,plain,
( 'big$uf'(g(X0,X1),X1)
| ~ 'big$uf'(X0,X1)
| ~ 'big$uf'(X0,a) ),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c3,plain,
( ~ 'big$uf'(X2,X1)
| ~ 'big$uf'(X2,g(X0,X1))
| ~ 'big$uf'(X0,X1)
| ~ 'big$uf'(X0,a) ),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c4,plain,
( 'big$uf'(X0,a)
| 'big$uf'(X0,h(X0)) ),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c5,plain,
( 'big$uf'(X1,a)
| 'big$uf'(i(X1,X0),X0)
| ~ 'big$uf'(X0,h(X1)) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c6,plain,
( ~ 'big$uf'(X1,h(X0))
| 'big$uf'(i(X0,X1),h(X0))
| 'big$uf'(X0,a) ),
inference(clausification,[status(esa)],[clause_7]) ).
cnf(d0,plain,
'big$uf'(X0,f(X0)),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(d1,plain,
( g(X0,f(X1)) = X1
| ~ 'big$uf'(X0,a)
| ~ 'big$uf'(X0,f(X1)) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
( ~ 'big$uf'(X0,a)
| g(X0,f(X0)) = X0 ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'big$uf'(i(X0,g(X1,X2)),X2)
| ~ 'big$uf'(X1,a)
| ~ 'big$uf'(X1,X2)
| ~ 'big$uf'(g(X1,X2),h(X0))
| 'big$uf'(X0,a) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d4,plain,
( ~ 'big$uf'(g(X0,h(X1)),h(X1))
| 'big$uf'(X1,a)
| ~ 'big$uf'(g(X0,h(X1)),h(X1))
| 'big$uf'(X1,a)
| ~ 'big$uf'(X0,a)
| ~ 'big$uf'(X0,h(X1)) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( ~ 'big$uf'(X1,a)
| ~ 'big$uf'(X1,h(X0))
| ~ 'big$uf'(X1,h(X0))
| ~ 'big$uf'(X1,a)
| 'big$uf'(X0,a) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ 'big$uf'(X1,h(X0))
| 'big$uf'(X0,a)
| 'big$uf'(X0,a)
| ~ 'big$uf'(i(X0,X1),a) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( ~ 'big$uf'(a,h(X0))
| 'big$uf'(X0,a)
| 'big$uf'(X0,a)
| ~ 'big$uf'(a,h(X0)) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( 'big$uf'(a,a)
| 'big$uf'(a,a) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
g(a,f(a)) = a,
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ 'big$uf'(X0,f(a))
| ~ 'big$uf'(a,a)
| ~ 'big$uf'(a,f(a))
| ~ 'big$uf'(X0,a) ),
inference(superposition,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
( ~ 'big$uf'(a,a)
| ~ 'big$uf'(X0,a)
| ~ 'big$uf'(X0,f(a)) ),
inference(resolution,[status(thm)],[d0,d10]) ).
cnf(d12,plain,
( ~ 'big$uf'(X0,a)
| ~ 'big$uf'(X0,f(a)) ),
inference(resolution,[status(thm)],[d8,d11]) ).
cnf(d13,plain,
~ 'big$uf'(a,a),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d8,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 17:10:48 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.18/2.99 % SZS status Unsatisfiable for theBenchmark.p
% 11.18/2.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------