%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET506-6 : 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 : n014.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 05:07:56 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 19 unt; 4 nHn; 24 RR)
% Number of literals : 65 ( 17 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(image,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
cnf(range_of,axiom,
domain_of(inverse(X1)) = range_of(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(inductive3,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive3) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
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(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(prove_universal_class_not_null_class_1,negated_conjecture,
universal_class = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_universal_class_not_null_class_1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
cnf(c_0_12,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
image ).
cnf(c_0_13,axiom,
domain_of(inverse(X1)) = range_of(X1),
range_of ).
cnf(c_0_14,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_15,axiom,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1) ),
inductive3 ).
cnf(c_0_16,plain,
domain_of(inverse(intersection(X1,cross_product(X2,universal_class)))) = image(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_18,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_19,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_20,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_21,negated_conjecture,
universal_class = null_class,
prove_universal_class_not_null_class_1 ).
cnf(c_0_22,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_23,plain,
( inductive(X1)
| ~ member(null_class,X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class)))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_24,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( member(universal_class,X1)
| ~ inductive(X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_27,plain,
( X1 = universal_class
| member(regular(X1),X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,plain,
( inductive(X1)
| ~ member(universal_class,X1)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class)))),X1) ),
inference(rw,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,plain,
( member(universal_class,universal_class)
| ~ inductive(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_31,plain,
( complement(X1) = universal_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( X1 = universal_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_33,plain,
( inductive(universal_class)
| ~ member(universal_class,universal_class) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,plain,
member(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ inductive(complement(X1))
| ~ member(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_36,plain,
complement(universal_class) = universal_class,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
inductive(universal_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_38,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET506-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n014.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 02:26:37 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------