%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET679+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n012.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 05:08:18 PM UTC 2026
% Result : Theorem 1.12s 1.64s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 106 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 121 ( 50 ~; 42 |; 11 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 3 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_46,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( not_equal(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p22,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(p21,axiom,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
<=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_46])]) ).
fof(c_0_8,plain,
! [X58,X59] :
( ( ~ not_equal(X58,X59)
| X58 != X59
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) )
& ( X58 = X59
| not_equal(X58,X59)
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_9,plain,
! [X93] : ilf_type(X93,set_type),
inference(variable_rename,[status(thm)],[p22]) ).
fof(c_0_10,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[p2]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p20]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ? [X2] : ilf_type(X2,member_type(X1)) ),
inference(fof_simplification,[status(thm)],[p21]) ).
fof(c_0_13,plain,
! [X47,X48] :
( ( ~ member(X48,X47)
| member(ordered_pair(X48,X48),identity_relation_of(X47))
| ~ ilf_type(X48,set_type)
| ~ ilf_type(X47,set_type) )
& ( ~ member(ordered_pair(X48,X48),identity_relation_of(X47))
| member(X48,X47)
| ~ ilf_type(X48,set_type)
| ~ ilf_type(X47,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
fof(c_0_14,negated_conjecture,
( ~ empty(esk10_0)
& ilf_type(esk10_0,set_type)
& ~ not_equal(identity_relation_of(esk10_0),empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_15,plain,
( X1 = X2
| not_equal(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_17,plain,
! [X49] :
( ~ ilf_type(X49,set_type)
| ~ member(X49,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
fof(c_0_18,plain,
! [X89,X90] :
( ( ~ ilf_type(X89,member_type(X90))
| member(X89,X90)
| empty(X90)
| ~ ilf_type(X90,set_type)
| ~ ilf_type(X89,set_type) )
& ( ~ member(X89,X90)
| ilf_type(X89,member_type(X90))
| empty(X90)
| ~ ilf_type(X90,set_type)
| ~ ilf_type(X89,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_19,plain,
! [X91] :
( empty(X91)
| ~ ilf_type(X91,set_type)
| ilf_type(esk9_1(X91),member_type(X91)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_20,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ not_equal(identity_relation_of(esk10_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16])]) ).
cnf(c_0_23,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( empty(X1)
| ilf_type(esk9_1(X1),member_type(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X2))
| ~ member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_16]),c_0_16])]) ).
cnf(c_0_27,negated_conjecture,
identity_relation_of(esk10_0) = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16])]) ).
cnf(c_0_29,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_16]),c_0_16])]) ).
cnf(c_0_30,plain,
( empty(X1)
| ilf_type(esk9_1(X1),member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16])]) ).
cnf(c_0_31,negated_conjecture,
~ member(X1,esk10_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
( empty(X1)
| member(esk9_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET679+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.07 % 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
% 0.06/0.26 % Computer : n012.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 5 02:31:46 EDT 2026
% 0.06/0.27 % CPUTime :
% 0.06/0.27 % start to proof: theBenchmark
% 1.12/1.64 % Version : CSE_E---1.7
% 1.12/1.64 % Problem : theBenchmark.p
% 1.12/1.64 % SZS status Theorem for theBenchmark.p
% 1.12/1.64 % SZS output start CNFRefutation
% See solution above
% 1.12/1.64 % Total time : 1.361s
%------------------------------------------------------------------------------