%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET031-4 : 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 : n003.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 05:06:58 PM UTC 2026
% Result : Unsatisfiable 6.85s 4.65s
% Output : CNFRefutation 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 9 unt; 2 nHn; 16 RR)
% Number of literals : 45 ( 11 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(ordered_pair_predicate4,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate4) ).
cnf(compose4,axiom,
( X1 = ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose4) ).
cnf(compose1,axiom,
( little_set(f29(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose1) ).
cnf(compose2,axiom,
( little_set(f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',compose2) ).
cnf(relation2,axiom,
( relation(X1)
| member(f18(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation2) ).
cnf(relation3,axiom,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation3) ).
cnf(prove_composition_is_a_relation,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_composition_is_a_relation) ).
cnf(c_0_9,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_10,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_11,axiom,
( ordered_pair_predicate(X1)
| ~ little_set(X2)
| ~ little_set(X3)
| X1 != ordered_pair(X2,X3) ),
ordered_pair_predicate4 ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
( X1 = ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
compose4 ).
cnf(c_0_14,plain,
( ordered_pair_predicate(X1)
| X1 != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X3))
| ~ little_set(X3)
| ~ little_set(X2) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( X1 = non_ordered_pair(non_ordered_pair(f29(X1,X2,X3),f29(X1,X2,X3)),non_ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)))
| ~ member(X1,compose(X2,X3)) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_16,axiom,
( little_set(f29(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
compose1 ).
cnf(c_0_17,axiom,
( little_set(f30(X1,X2,X3))
| ~ member(X1,compose(X2,X3)) ),
compose2 ).
cnf(c_0_18,plain,
( ordered_pair_predicate(X1)
| ~ member(X1,compose(X2,X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]),c_0_16]),c_0_17]) ).
cnf(c_0_19,axiom,
( relation(X1)
| member(f18(X1),X1) ),
relation2 ).
cnf(c_0_20,axiom,
( relation(X1)
| ~ ordered_pair_predicate(f18(X1)) ),
relation3 ).
cnf(c_0_21,negated_conjecture,
~ relation(compose(a,b)),
prove_composition_is_a_relation ).
cnf(c_0_22,plain,
relation(compose(X1,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET031-4 : TPTP v9.2.1. Released v1.0.0.
% 0.11/0.13 % 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
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 02:05:26 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 6.85/4.65 % Version : CSE_E---1.7
% 6.85/4.65 % Problem : theBenchmark.p
% 6.85/4.65 % SZS status Unsatisfiable for theBenchmark.p
% 6.85/4.65 % SZS output start CNFRefutation
% See solution above
% 6.85/4.67 % Total time : 3.371s
%------------------------------------------------------------------------------