%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET022-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:54 PM UTC 2026
% Result : Unsatisfiable 63.63s 41.86s
% Output : CNFRefutation 64.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 5 unt; 0 nHn; 15 RR)
% Number of literals : 27 ( 5 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_first,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
cnf(ordered_pair_predicate3,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).
cnf(ordered_pair_predicate1,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).
cnf(ordered_pair_predicate2,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).
cnf(prove_first_component_is_small,negated_conjecture,
~ little_set(first(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_component_is_small) ).
cnf(an_ordered_pair_predicate,hypothesis,
ordered_pair_predicate(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
cnf(c_0_6,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_first ).
cnf(c_0_7,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate3 ).
cnf(c_0_8,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate1 ).
cnf(c_0_9,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate2 ).
cnf(c_0_10,plain,
( f2(X1) = first(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]) ).
cnf(c_0_11,negated_conjecture,
~ little_set(first(a)),
prove_first_component_is_small ).
cnf(c_0_12,plain,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_13,hypothesis,
ordered_pair_predicate(a),
an_ordered_pair_predicate ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET022-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 02:05:16 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 63.63/41.86 % Version : CSE_E---1.7
% 63.63/41.86 % Problem : theBenchmark.p
% 63.63/41.86 % SZS status Unsatisfiable for theBenchmark.p
% 63.63/41.86 % SZS output start CNFRefutation
% See solution above
% 64.03/42.20 % Total time : 28.412s
%------------------------------------------------------------------------------