%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM139-1 : 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 : n024.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 04:52:52 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.65s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 20 unt; 2 nHn; 10 RR)
% Number of literals : 28 ( 12 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(power_class_definition,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',power_class_definition) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(prove_complete_induction3_2,negated_conjecture,
~ subclass(intersection(power_class(x),z),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_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(prove_complete_induction3_1,negated_conjecture,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_complete_induction3_1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(c_0_9,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_10,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_11,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_12,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
power_class_definition ).
cnf(c_0_13,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_14,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_15,negated_conjecture,
~ subclass(intersection(power_class(x),z),x),
prove_complete_induction3_2 ).
cnf(c_0_16,plain,
complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))) = power_class(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
~ subclass(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_19,negated_conjecture,
~ member(not_subclass_element(intersection(power_class(x),z),x),z),
prove_complete_induction3_1 ).
cnf(c_0_20,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_21,negated_conjecture,
member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
~ member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),z),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM139-1 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 19:15:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.24 % start to proof: theBenchmark
% 1.25/1.65 % Version : CSE_E---1.7
% 1.25/1.65 % Problem : theBenchmark.p
% 1.25/1.65 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.65 % SZS output start CNFRefutation
% See solution above
% 1.25/1.65 % Total time : 1.361s
%------------------------------------------------------------------------------