%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET238-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 05:07:38 PM UTC 2026
% Result : Unsatisfiable 1.48s 1.79s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 16 unt; 0 nHn; 14 RR)
% Number of literals : 26 ( 11 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_corollary_to_restriction_alternate_defn1_1,negated_conjecture,
member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_1) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(prove_corollary_to_restriction_alternate_defn1_2,negated_conjecture,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_restriction_alternate_defn1_2) ).
cnf(c_0_7,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_8,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_9,negated_conjecture,
member(z,restrict(xr,x,y)),
prove_corollary_to_restriction_alternate_defn1_1 ).
cnf(c_0_10,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_11,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_12,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_13,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_14,negated_conjecture,
member(z,intersection(xr,cross_product(x,y))),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
prove_corollary_to_restriction_alternate_defn1_2 ).
cnf(c_0_16,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
member(z,cross_product(x,y)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ member(unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))),intersection(xr,cross_product(x,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_10]),c_0_12]) ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(first(z),first(z)),unordered_pair(first(z),unordered_pair(second(z),second(z)))) = z,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET238-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n011.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 02:15:32 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.48/1.79 % Version : CSE_E---1.7
% 1.48/1.79 % Problem : theBenchmark.p
% 1.48/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.48/1.79 % SZS output start CNFRefutation
% See solution above
% 1.48/1.79 % Total time : 1.369s
%------------------------------------------------------------------------------