%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET022-3 : 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 : n013.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 08:31:38 AM UTC 2026
% Result : Unsatisfiable 75.08s 14.08s
% Output : CNFRefutation 75.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 11 unt; 0 nHn; 20 RR)
% Number of literals : 31 ( 8 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_first,axiom,
( first('ordered$upair'(X0,X1)) = X0
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ) ).
cnf(an_ordered_pair_predicate,hypothesis,
'ordered$upair$upredicate'(a) ).
cnf(prove_first_component_is_small,negated_conjecture,
~ 'little$uset'(first(a)) ).
cnf(ordered_pair_predicate1,axiom,
( 'little$uset'(f2(X0))
| ~ 'ordered$upair$upredicate'(X0) ) ).
cnf(ordered_pair_predicate2,axiom,
( 'little$uset'(f3(X0))
| ~ 'ordered$upair$upredicate'(X0) ) ).
cnf(ordered_pair_predicate3,axiom,
( X0 = 'ordered$upair'(f2(X0),f3(X0))
| ~ 'ordered$upair$upredicate'(X0) ) ).
cnf(c4,plain,
( first('ordered$upair'(X1,X0)) = X1
| ~ 'little$uset'(X1)
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[property_of_first]) ).
cnf(c6,plain,
'ordered$upair$upredicate'(a),
inference(clausification,[status(esa)],[an_ordered_pair_predicate]) ).
cnf(c7,plain,
~ 'little$uset'(first(a)),
inference(clausification,[status(esa)],[prove_first_component_is_small]) ).
cnf(c18,plain,
( 'little$uset'(f2(X0))
| ~ 'ordered$upair$upredicate'(X0) ),
inference(clausification,[status(esa)],[ordered_pair_predicate1]) ).
cnf(c19,plain,
( 'little$uset'(f3(X0))
| ~ 'ordered$upair$upredicate'(X0) ),
inference(clausification,[status(esa)],[ordered_pair_predicate2]) ).
cnf(c20,plain,
( 'ordered$upair'(f2(X0),f3(X0)) = X0
| ~ 'ordered$upair$upredicate'(X0) ),
inference(clausification,[status(esa)],[ordered_pair_predicate3]) ).
cnf(d0,plain,
'ordered$upair'(f2(a),f3(a)) = a,
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(d1,plain,
'little$uset'(f3(a)),
inference(resolution,[status(thm)],[c19,c6]) ).
cnf(d2,plain,
'little$uset'(f2(a)),
inference(resolution,[status(thm)],[c18,c6]) ).
cnf(d3,plain,
( ~ 'little$uset'(X0)
| first('ordered$upair'(f2(a),X0)) = f2(a) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
first('ordered$upair'(f2(a),f3(a))) = f2(a),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
first(a) = f2(a),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
'little$uset'(first(a)),
inference(demodulation,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c7,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 06:52:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.08/14.08 % SZS status Unsatisfiable for theBenchmark.p
% 75.08/14.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------