%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET096-7 : 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 : n027.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 05:07:17 PM UTC 2026
% Result : Unsatisfiable 2.05s 2.00s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 18 unt; 2 nHn; 24 RR)
% Number of literals : 58 ( 16 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(singleton_in_unordered_pair2,axiom,
subclass(singleton(X1),unordered_pair(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(transitivity_of_subclass,axiom,
( subclass(X1,X3)
| ~ subclass(X1,X2)
| ~ subclass(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
cnf(prove_two_subsets_of_singleton_1,negated_conjecture,
subclass(x,singleton(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_1) ).
cnf(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
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(prove_two_subsets_of_singleton_3,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_3) ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_two_subsets_of_singleton_2,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_two_subsets_of_singleton_2) ).
cnf(unordered_pair_is_subset,axiom,
( subclass(unordered_pair(X1,X3),X2)
| ~ member(X1,X2)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
cnf(c_0_11,axiom,
subclass(singleton(X1),unordered_pair(X2,X1)),
singleton_in_unordered_pair2 ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,axiom,
( subclass(X1,X3)
| ~ subclass(X1,X2)
| ~ subclass(X2,X3) ),
transitivity_of_subclass ).
cnf(c_0_14,plain,
subclass(unordered_pair(X1,X1),unordered_pair(X2,X1)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
subclass(x,singleton(y)),
prove_two_subsets_of_singleton_1 ).
cnf(c_0_16,plain,
( subclass(X1,unordered_pair(X2,X3))
| ~ subclass(X1,unordered_pair(X3,X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
subclass(x,unordered_pair(y,y)),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_18,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(c_0_19,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_20,negated_conjecture,
subclass(x,unordered_pair(X1,y)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
singleton(y) != x,
prove_two_subsets_of_singleton_3 ).
cnf(c_0_22,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( member(X1,unordered_pair(X2,y))
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_25,negated_conjecture,
unordered_pair(y,y) != x,
inference(rw,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
( X1 = y
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_28,negated_conjecture,
x != null_class,
prove_two_subsets_of_singleton_2 ).
cnf(c_0_29,negated_conjecture,
~ subclass(unordered_pair(y,y),x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_25]) ).
cnf(c_0_30,axiom,
( subclass(unordered_pair(X1,X3),X2)
| ~ member(X1,X2)
| ~ member(X3,X2) ),
unordered_pair_is_subset ).
cnf(c_0_31,negated_conjecture,
regular(x) = y,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ member(y,x),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_31]),c_0_28]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET096-7 : 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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:12:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.05/2.00 % Version : CSE_E---1.7
% 2.05/2.00 % Problem : theBenchmark.p
% 2.05/2.00 % SZS status Unsatisfiable for theBenchmark.p
% 2.05/2.00 % SZS output start CNFRefutation
% See solution above
% 2.05/2.01 % Total time : 1.372s
%------------------------------------------------------------------------------