%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM095-1 : 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 : n002.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 04:52:50 PM UTC 2026
% Result : Unsatisfiable 63.16s 36.76s
% Output : CNFRefutation 63.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 64 ( 23 unt; 16 nHn; 44 RR)
% Number of literals : 120 ( 17 equ; 50 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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(well_ordering2,axiom,
( X3 = null_class
| member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',well_ordering2) ).
cnf(prove_sections_property4_1,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_sections_property4_3,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(section1,axiom,
( subclass(X2,X3)
| ~ section(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',section1) ).
cnf(prove_sections_property4_2,negated_conjecture,
section(xr,w,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_2) ).
cnf(prove_sections_property4_4,negated_conjecture,
y != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sections_property4_4) ).
cnf(c_0_17,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_18,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_19,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_20,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_21,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_24,plain,
( subclass(intersection(X1,X2),intersection(X3,X1))
| ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_26,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_27,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_28,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_29,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( X3 = null_class
| member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2) ),
well_ordering2 ).
cnf(c_0_31,negated_conjecture,
well_ordering(xr,y),
prove_sections_property4_1 ).
cnf(c_0_32,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_33,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_34,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),complement(w)),
prove_sections_property4_3 ).
cnf(c_0_36,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29])]) ).
cnf(c_0_37,negated_conjecture,
( X1 = null_class
| member(least(xr,X1),X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_40,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_41,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_42,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_43,negated_conjecture,
~ member(least(xr,intersection(y,complement(w))),complement(w)),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( intersection(X1,X2) = null_class
| member(least(xr,intersection(X1,X2)),X2)
| ~ subclass(intersection(X1,X2),y) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_45,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_46,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_41]),c_0_42]) ).
cnf(c_0_49,negated_conjecture,
intersection(y,complement(w)) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_50,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_46]),c_0_34]) ).
cnf(c_0_51,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_17,c_0_47]) ).
cnf(c_0_52,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_53,axiom,
( subclass(X2,X3)
| ~ section(X1,X2,X3) ),
section1 ).
cnf(c_0_54,negated_conjecture,
section(xr,w,y),
prove_sections_property4_2 ).
cnf(c_0_55,negated_conjecture,
( ~ member(X1,complement(w))
| ~ member(X1,y) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_49]),c_0_50]) ).
cnf(c_0_56,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_28,c_0_51]) ).
cnf(c_0_57,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_52,c_0_20]) ).
cnf(c_0_58,negated_conjecture,
subclass(w,y),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
y != w,
prove_sections_property4_4 ).
cnf(c_0_60,negated_conjecture,
( subclass(y,X1)
| ~ member(not_subclass_element(y,X1),complement(w)) ),
inference(spm,[status(thm)],[c_0_55,c_0_20]) ).
cnf(c_0_61,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_62,negated_conjecture,
~ subclass(y,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_48]),c_0_61]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM095-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.10 % 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
% 0.13/0.30 % Computer : n002.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue May 5 00:10:33 EDT 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.31 % start to proof: theBenchmark
% 63.16/36.76 % Version : CSE_E---1.7
% 63.16/36.76 % Problem : theBenchmark.p
% 63.16/36.76 % SZS status Unsatisfiable for theBenchmark.p
% 63.16/36.76 % SZS output start CNFRefutation
% See solution above
% 63.37/37.00 % Total time : 27.430s
%------------------------------------------------------------------------------