%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET075-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 : n008.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 05:07:10 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.94s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 18 unt; 4 nHn; 23 RR)
% Number of literals : 57 ( 15 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(prove_corollary_to_unordered_pair_axiom3_1,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(prove_corollary_to_unordered_pair_axiom3_2,negated_conjecture,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(c_0_11,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_14,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_11,c_0_12]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
member(ordered_pair(x,y),cross_product(u,v)),
prove_corollary_to_unordered_pair_axiom3_1 ).
cnf(c_0_16,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_21,negated_conjecture,
unordered_pair(x,y) = null_class,
prove_corollary_to_unordered_pair_axiom3_2 ).
cnf(c_0_22,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
member(y,v),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_25,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_26,negated_conjecture,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
member(y,universal_class),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
member(y,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_30,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_31,negated_conjecture,
( X1 = null_class
| member(y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( complement(X1) = null_class
| ~ member(y,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
complement(null_class) = null_class,
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
~ member(X1,null_class),
inference(spm,[status(thm)],[c_0_30,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_29,c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.32 % Problem : SET075-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.04/0.32 % 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
% 0.15/0.53 % Computer : n008.cluster.edu
% 0.15/0.53 % Model : x86_64 x86_64
% 0.15/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.53 % Memory : 8042.1875MB
% 0.15/0.53 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.53 % CPULimit : 300
% 0.15/0.53 % WCLimit : 300
% 0.15/0.53 % DateTime : Tue May 5 02:09:13 EDT 2026
% 0.15/0.53 % CPUTime :
% 0.15/0.54 % start to proof: theBenchmark
% 1.33/1.94 % Version : CSE_E---1.7
% 1.33/1.94 % Problem : theBenchmark.p
% 1.33/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.94 % SZS output start CNFRefutation
% See solution above
% 1.33/1.94 % Total time : 1.373s
%------------------------------------------------------------------------------