%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET157-6 : 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 : n029.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 05:07:28 PM UTC 2026
% Result : Unsatisfiable 1.48s 1.80s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 17 unt; 10 nHn; 30 RR)
% Number of literals : 79 ( 17 equ; 34 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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_complement_is_unique_1,negated_conjecture,
union(x,y) = universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complement_is_unique_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
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(prove_complement_is_unique_2,negated_conjecture,
intersection(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complement_is_unique_2) ).
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(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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
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_complement_is_unique_3,negated_conjecture,
complement(x) != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complement_is_unique_3) ).
cnf(c_0_13,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_14,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_15,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_16,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_17,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
union(x,y) = universal_class,
prove_complement_is_unique_1 ).
cnf(c_0_19,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_20,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
complement(intersection(complement(x),complement(y))) = universal_class,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( ~ member(X1,intersection(complement(x),complement(y)))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_25,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_26,negated_conjecture,
intersection(x,y) = null_class,
prove_complement_is_unique_2 ).
cnf(c_0_27,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_17]) ).
cnf(c_0_28,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_29,negated_conjecture,
intersection(complement(x),complement(y)) = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_16]),c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(X1,y)
| ~ member(X1,x) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_31,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_32,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_33,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
( ~ member(X1,complement(y))
| ~ member(X1,complement(x)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( subclass(y,X1)
| ~ member(not_subclass_element(y,X1),x) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_36,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( member(X1,y)
| ~ member(X1,complement(x)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_17]) ).
cnf(c_0_38,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_39,negated_conjecture,
subclass(y,complement(x)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
complement(x) != y,
prove_complement_is_unique_3 ).
cnf(c_0_41,negated_conjecture,
( member(not_subclass_element(complement(x),X1),y)
| subclass(complement(x),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_42,negated_conjecture,
~ subclass(complement(x),y),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET157-6 : 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
% 0.15/0.32 % Computer : n029.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:13:59 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.48/1.80 % Version : CSE_E---1.7
% 1.48/1.80 % Problem : theBenchmark.p
% 1.48/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.48/1.80 % SZS output start CNFRefutation
% See solution above
% 1.59/1.80 % Total time : 1.372s
%------------------------------------------------------------------------------