%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU425+1 : TPTP v9.2.1. Released v3.4.0.
% 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 : n010.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 05:12:17 PM UTC 2026
% Result : Theorem 5.65s 4.39s
% Output : CNFRefutation 5.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 13 unt; 0 def)
% Number of atoms : 184 ( 48 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 218 ( 87 ~; 90 |; 22 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 7 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> ( ( ( X2 = k1_xboole_0
=> X1 = k1_xboole_0 )
=> ( v1_funct_2(X3,X1,X2)
<=> X1 = k4_relset_1(X1,X2,X3) ) )
& ( X2 = k1_xboole_0
=> ( X1 = k1_xboole_0
| ( v1_funct_2(X3,X1,X2)
<=> X3 = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> k4_relset_1(X1,X2,X3) = k1_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(d3_relset_2,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ! [X3] :
( ( v1_relat_1(X3)
& v1_funct_1(X3) )
=> ( X3 = k5_relset_2(X1,X2)
<=> ( k1_relat_1(X3) = k1_zfmisc_1(X1)
& ! [X4] :
( r1_tarski(X4,X1)
=> k1_funct_1(X3,X4) = k9_relat_1(X2,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relset_2) ).
fof(dt_k5_relset_2,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( v1_relat_1(k5_relset_2(X1,X2))
& v1_funct_1(k5_relset_2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(t21_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( v1_funct_1(k5_relset_2(X1,X3))
& v1_funct_2(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& m2_relset_1(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(t20_relset_2,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> r1_tarski(k2_relat_1(k5_relset_2(X1,X3)),k1_zfmisc_1(k2_relat_1(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).
fof(t11_relset_1,axiom,
! [X1,X2,X3] :
( v1_relat_1(X3)
=> ( ( r1_tarski(k1_relat_1(X3),X1)
& r1_tarski(k2_relat_1(X3),X2) )
=> m2_relset_1(X3,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(fc12_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_12,plain,
! [X96,X97,X98] :
( ( ~ v1_funct_2(X98,X96,X97)
| X96 = k4_relset_1(X96,X97,X98)
| X97 = k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) )
& ( X96 != k4_relset_1(X96,X97,X98)
| v1_funct_2(X98,X96,X97)
| X97 = k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) )
& ( ~ v1_funct_2(X98,X96,X97)
| X96 = k4_relset_1(X96,X97,X98)
| X96 != k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) )
& ( X96 != k4_relset_1(X96,X97,X98)
| v1_funct_2(X98,X96,X97)
| X96 != k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) )
& ( ~ v1_funct_2(X98,X96,X97)
| X98 = k1_xboole_0
| X96 = k1_xboole_0
| X97 != k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) )
& ( X98 != k1_xboole_0
| v1_funct_2(X98,X96,X97)
| X96 = k1_xboole_0
| X97 != k1_xboole_0
| ~ m2_relset_1(X98,X96,X97) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
fof(c_0_13,plain,
! [X139,X140,X141] :
( ~ m1_relset_1(X141,X139,X140)
| k4_relset_1(X139,X140,X141) = k1_relat_1(X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_14,plain,
! [X142,X143,X144] :
( ( ~ m2_relset_1(X144,X142,X143)
| m1_relset_1(X144,X142,X143) )
& ( ~ m1_relset_1(X144,X142,X143)
| m2_relset_1(X144,X142,X143) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_15,plain,
! [X99,X100,X101,X102] :
( ( k1_relat_1(X101) = k1_zfmisc_1(X99)
| X101 != k5_relset_2(X99,X100)
| ~ v1_relat_1(X101)
| ~ v1_funct_1(X101)
| ~ v1_relat_1(X100) )
& ( ~ r1_tarski(X102,X99)
| k1_funct_1(X101,X102) = k9_relat_1(X100,X102)
| X101 != k5_relset_2(X99,X100)
| ~ v1_relat_1(X101)
| ~ v1_funct_1(X101)
| ~ v1_relat_1(X100) )
& ( r1_tarski(esk4_3(X99,X100,X101),X99)
| k1_relat_1(X101) != k1_zfmisc_1(X99)
| X101 = k5_relset_2(X99,X100)
| ~ v1_relat_1(X101)
| ~ v1_funct_1(X101)
| ~ v1_relat_1(X100) )
& ( k1_funct_1(X101,esk4_3(X99,X100,X101)) != k9_relat_1(X100,esk4_3(X99,X100,X101))
| k1_relat_1(X101) != k1_zfmisc_1(X99)
| X101 = k5_relset_2(X99,X100)
| ~ v1_relat_1(X101)
| ~ v1_funct_1(X101)
| ~ v1_relat_1(X100) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relset_2])])])])]) ).
fof(c_0_16,plain,
! [X107,X108] :
( ( v1_relat_1(k5_relset_2(X107,X108))
| ~ v1_relat_1(X108) )
& ( v1_funct_1(k5_relset_2(X107,X108))
| ~ v1_relat_1(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relset_2])])]) ).
cnf(c_0_17,plain,
( v1_funct_2(X3,X1,X2)
| X2 = k1_xboole_0
| X1 != k4_relset_1(X1,X2,X3)
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( k4_relset_1(X2,X3,X1) = k1_relat_1(X1)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( m2_relset_1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( k1_relat_1(X1) = k1_zfmisc_1(X2)
| X1 != k5_relset_2(X2,X3)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( v1_funct_1(k5_relset_2(X1,X2))
| ~ v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( v1_relat_1(k5_relset_2(X1,X2))
| ~ v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( v1_funct_1(k5_relset_2(X1,X3))
& v1_funct_2(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& m2_relset_1(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3))) ) ),
inference(assume_negation,[status(cth)],[t21_relset_2]) ).
cnf(c_0_24,plain,
( X1 = k1_xboole_0
| v1_funct_2(X2,k1_relat_1(X2),X1)
| ~ m1_relset_1(X2,k1_relat_1(X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]),c_0_19]) ).
cnf(c_0_25,plain,
( k1_relat_1(k5_relset_2(X1,X2)) = k1_zfmisc_1(X1)
| ~ v1_relat_1(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),c_0_22]) ).
fof(c_0_26,plain,
! [X93,X94,X95] :
( ~ m1_subset_1(X95,k1_zfmisc_1(k2_zfmisc_1(X93,X94)))
| v1_relat_1(X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_27,negated_conjecture,
( m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
& ( ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0))
| ~ v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0)))
| ~ m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
fof(c_0_28,plain,
! [X151,X152,X153] :
( ~ m1_subset_1(X153,k1_zfmisc_1(k2_zfmisc_1(X151,X152)))
| r1_tarski(k2_relat_1(k5_relset_2(X151,X153)),k1_zfmisc_1(k2_relat_1(X153))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relset_2])]) ).
cnf(c_0_29,plain,
( X1 = k1_xboole_0
| v1_funct_2(k5_relset_2(X2,X3),k1_zfmisc_1(X2),X1)
| ~ m1_relset_1(k5_relset_2(X2,X3),k1_zfmisc_1(X2),X1)
| ~ v1_relat_1(X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,plain,
( v1_relat_1(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X146,X147,X148] :
( ~ v1_relat_1(X148)
| ~ r1_tarski(k1_relat_1(X148),X146)
| ~ r1_tarski(k2_relat_1(X148),X147)
| m2_relset_1(X148,X146,X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t11_relset_1])]) ).
cnf(c_0_34,plain,
( r1_tarski(k2_relat_1(k5_relset_2(X2,X1)),k1_zfmisc_1(k2_relat_1(X1)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0))
| ~ v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0)))
| ~ m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
( X1 = k1_xboole_0
| v1_funct_2(k5_relset_2(X2,X3),k1_zfmisc_1(X2),X1)
| ~ v1_relat_1(X3)
| ~ m2_relset_1(k5_relset_2(X2,X3),k1_zfmisc_1(X2),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
v1_relat_1(esk3_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( m2_relset_1(X1,X2,X3)
| ~ v1_relat_1(X1)
| ~ r1_tarski(k1_relat_1(X1),X2)
| ~ r1_tarski(k2_relat_1(X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
r1_tarski(k2_relat_1(k5_relset_2(esk1_0,esk3_0)),k1_zfmisc_1(k2_relat_1(esk3_0))),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( k1_zfmisc_1(k2_relat_1(esk3_0)) = k1_xboole_0
| ~ m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0)))
| ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
( m2_relset_1(k5_relset_2(esk1_0,esk3_0),X1,k1_zfmisc_1(k2_relat_1(esk3_0)))
| ~ r1_tarski(k1_relat_1(k5_relset_2(esk1_0,esk3_0)),X1)
| ~ v1_relat_1(k5_relset_2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_42,plain,
! [X145] : r1_tarski(X145,X145),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_43,negated_conjecture,
( k1_zfmisc_1(k2_relat_1(esk3_0)) = k1_xboole_0
| ~ r1_tarski(k1_relat_1(k5_relset_2(esk1_0,esk3_0)),k1_zfmisc_1(esk1_0))
| ~ v1_relat_1(k5_relset_2(esk1_0,esk3_0))
| ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_45,plain,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_46,negated_conjecture,
( k1_zfmisc_1(k2_relat_1(esk3_0)) = k1_xboole_0
| ~ v1_relat_1(k5_relset_2(esk1_0,esk3_0))
| ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_25]),c_0_44]),c_0_37])]) ).
fof(c_0_47,plain,
! [X120] : ~ v1_xboole_0(k1_zfmisc_1(X120)),
inference(variable_rename,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( k1_zfmisc_1(k2_relat_1(esk3_0)) = k1_xboole_0
| ~ v1_relat_1(k5_relset_2(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_37])]) ).
cnf(c_0_49,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
k1_zfmisc_1(k2_relat_1(esk3_0)) = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_22]),c_0_37])]) ).
cnf(c_0_51,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU425+1 : TPTP v9.2.1. Released v3.4.0.
% 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
% 0.16/0.33 % Computer : n010.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 03:10:22 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.65/4.39 % Version : CSE_E---1.7
% 5.65/4.39 % Problem : theBenchmark.p
% 5.65/4.39 % SZS status Theorem for theBenchmark.p
% 5.65/4.39 % SZS output start CNFRefutation
% See solution above
% 5.75/4.41 % Total time : 3.370s
%------------------------------------------------------------------------------