%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET230-6 : 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 : n025.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 05:07:37 PM UTC 2026
% Result : Unsatisfiable 1.68s 1.88s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 54 ( 17 unt; 15 nHn; 39 RR)
% Number of literals : 108 ( 29 equ; 43 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 14 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(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(prove_corollary_to_cross_product_cancellation_1,negated_conjecture,
cross_product(u,u) = cross_product(w,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_cross_product_cancellation_1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(not_subclass_members1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_corollary_to_cross_product_cancellation_2,negated_conjecture,
u != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_cross_product_cancellation_2) ).
cnf(c_0_13,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_14,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_15,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_16,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_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_18,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
cross_product(u,u) = cross_product(w,w),
prove_corollary_to_cross_product_cancellation_1 ).
cnf(c_0_20,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_17,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(w,w))
| ~ member(X2,u)
| ~ member(X1,u) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,w)
| ~ member(X1,u)
| ~ member(X2,u) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_24,negated_conjecture,
( member(X1,u)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),cross_product(w,w)) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( u = null_class
| member(regular(u),w)
| ~ member(X1,u) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( member(X1,u)
| ~ member(X1,w)
| ~ member(X2,w) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( u = null_class
| member(regular(u),w) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_28,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_29,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_30,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_31,negated_conjecture,
( u = null_class
| member(X1,u)
| ~ member(X1,w) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_33,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( w = null_class
| member(X1,u)
| ~ member(X1,w) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_35,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_36,negated_conjecture,
( u = null_class
| subclass(X1,u)
| ~ member(not_subclass_element(X1,u),w) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_38,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_39,negated_conjecture,
( w = null_class
| subclass(X1,u)
| ~ member(not_subclass_element(X1,u),w) ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( member(not_subclass_element(u,X1),w)
| subclass(u,X1)
| ~ member(X2,u) ),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_41,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_42,negated_conjecture,
( u = null_class
| subclass(w,u) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_43,negated_conjecture,
u != w,
prove_corollary_to_cross_product_cancellation_2 ).
cnf(c_0_44,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( w = null_class
| subclass(w,u) ),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_46,negated_conjecture,
( u = null_class
| member(not_subclass_element(u,X1),w)
| subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_47,negated_conjecture,
( u = null_class
| ~ subclass(u,w) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_48,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_33]) ).
cnf(c_0_49,negated_conjecture,
( w = null_class
| ~ subclass(u,w) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_45]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
u = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_47]) ).
cnf(c_0_51,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_52,negated_conjecture,
w = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_50]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET230-6 : 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
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:16:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.68/1.88 % Version : CSE_E---1.7
% 1.68/1.88 % Problem : theBenchmark.p
% 1.68/1.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.68/1.88 % SZS output start CNFRefutation
% See solution above
% 1.68/1.88 % Total time : 1.370s
%------------------------------------------------------------------------------