%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU425+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:29:22 PM UTC 2026
% Result : Theorem 0.26s 29.51s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 98 ( 50 unt; 0 def)
% Number of atoms : 230 ( 72 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 228 ( 96 ~; 83 |; 28 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 143 ( 15 sgn 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t21_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( m2_relset_1(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& v1_funct_2(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& v1_funct_1(k5_relset_2(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relset_2) ).
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/sandbox2/benchmark/theBenchmark.p',t20_relset_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t10_relset_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(k2_relat_1(X2),X1)
=> m2_relset_1(X2,k1_relat_1(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',t10_relset_1) ).
fof(t3_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t3_relat_1) ).
fof(t6_relat_1,axiom,
! [X1,X2] : v1_relat_1(k2_zfmisc_1(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t6_relat_1) ).
fof(dt_k5_relset_2,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( v1_funct_1(k5_relset_2(X1,X2))
& v1_relat_1(k5_relset_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(d3_relset_2,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ! [X3] :
( ( v1_funct_1(X3)
& v1_relat_1(X3) )
=> ( X3 = k5_relset_2(X1,X2)
<=> ( ! [X4] :
( r1_tarski(X4,X1)
=> k1_funct_1(X3,X4) = k9_relat_1(X2,X4) )
& k1_relat_1(X3) = k1_zfmisc_1(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relset_2) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',dt_m2_relset_1) ).
fof(t25_relat_1,axiom,
! [X1] :
( v1_relat_1(X1)
=> ! [X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> ( r1_tarski(k2_relat_1(X1),k2_relat_1(X2))
& r1_tarski(k1_relat_1(X1),k1_relat_1(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t25_relat_1) ).
fof(t1_card_5,axiom,
( np__2 = k2_tarski(np__0,np__1)
& np__1 = k1_tarski(np__0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+153.ax',t1_card_5) ).
fof(t51_card_1,axiom,
np__0 = k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+54.ax',t51_card_1) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',cc1_relset_1) ).
fof(t83_zfmisc_1,axiom,
! [X1,X2] : k1_zfmisc_1(k3_xboole_0(X1,X2)) = k3_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+6.ax',t83_zfmisc_1) ).
fof(t1_zfmisc_1,axiom,
k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+6.ax',t1_zfmisc_1) ).
fof(t2_boole,axiom,
! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+3.ax',t2_boole) ).
fof(t49_zfmisc_1,axiom,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+6.ax',t49_zfmisc_1) ).
fof(t4_funct_2,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( r1_tarski(k2_relat_1(X2),X1)
=> ( m2_relset_1(X2,k1_relat_1(X2),X1)
& v1_funct_2(X2,k1_relat_1(X2),X1)
& v1_funct_1(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+20.ax',t4_funct_2) ).
fof(t22_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(X1,k3_xboole_0(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t22_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(t1_boole,axiom,
! [X1] : k2_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+3.ax',t1_boole) ).
fof(t12_sysrel,axiom,
! [X1,X2] :
~ ( ~ ( k2_relat_1(k2_zfmisc_1(X1,X2)) = X2
& k1_relat_1(k2_zfmisc_1(X1,X2)) = X1 )
& X2 != k1_xboole_0
& X1 != k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+126.ax',t12_sysrel) ).
fof(t15_xboole_1,axiom,
! [X1,X2] :
( k2_xboole_0(X1,X2) = k1_xboole_0
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t15_xboole_1) ).
fof(c_0_23,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( m2_relset_1(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& v1_funct_2(k5_relset_2(X1,X3),k1_zfmisc_1(X1),k1_zfmisc_1(k2_relat_1(X3)))
& v1_funct_1(k5_relset_2(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[t21_relset_2]) ).
fof(c_0_24,plain,
! [X310,X311,X312] :
( r1_tarski(k2_relat_1(k5_relset_2(X310,X312)),k1_zfmisc_1(k2_relat_1(X312)))
| ~ m1_subset_1(X312,k1_zfmisc_1(k2_zfmisc_1(X310,X311))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relset_2])])]) ).
fof(c_0_25,negated_conjecture,
( ( ~ 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_2(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)) )
& m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
fof(c_0_26,plain,
! [X863,X864] :
( ( m1_subset_1(X863,k1_zfmisc_1(X864))
| ~ r1_tarski(X863,X864) )
& ( r1_tarski(X863,X864)
| ~ m1_subset_1(X863,k1_zfmisc_1(X864)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_27,plain,
! [X162,X163] :
( m2_relset_1(X163,k1_relat_1(X163),X162)
| ~ r1_tarski(k2_relat_1(X163),X162)
| ~ v1_relat_1(X163) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_relset_1])])]) ).
cnf(c_0_28,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| r1_tarski(k2_relat_1(k5_relset_2(X2,X1)),k1_zfmisc_1(k2_relat_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X445,X446] :
( v1_relat_1(X445)
| ~ r1_tarski(X445,X446)
| ~ v1_relat_1(X446) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_relat_1])])]) ).
cnf(c_0_31,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X351,X352] : v1_relat_1(k2_zfmisc_1(X351,X352)),
inference(variable_rename,[status(thm)],[t6_relat_1]) ).
cnf(c_0_33,plain,
( ~ r1_tarski(k2_relat_1(X1),X2)
| ~ v1_relat_1(X1)
| m2_relset_1(X1,k1_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,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_28,c_0_29]) ).
fof(c_0_35,plain,
! [X299,X300] :
( ( ~ v1_relat_1(X300)
| v1_funct_1(k5_relset_2(X299,X300)) )
& ( ~ v1_relat_1(X300)
| v1_relat_1(k5_relset_2(X299,X300)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relset_2])])])]) ).
cnf(c_0_36,plain,
( ~ r1_tarski(X2,X1)
| ~ v1_relat_1(X1)
| v1_relat_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
r1_tarski(esk3_0,k2_zfmisc_1(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_38,plain,
v1_relat_1(k2_zfmisc_1(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X301,X302,X303,X304] :
( ( ~ v1_relat_1(X302)
| ~ v1_funct_1(X303)
| ~ v1_relat_1(X303)
| X303 = k5_relset_2(X301,X302)
| k1_relat_1(X303) != k1_zfmisc_1(X301)
| k1_funct_1(X303,esk33_3(X301,X302,X303)) != k9_relat_1(X302,esk33_3(X301,X302,X303)) )
& ( ~ v1_relat_1(X302)
| ~ v1_funct_1(X303)
| ~ v1_relat_1(X303)
| X303 = k5_relset_2(X301,X302)
| k1_relat_1(X303) != k1_zfmisc_1(X301)
| r1_tarski(esk33_3(X301,X302,X303),X301) )
& ( ~ v1_relat_1(X302)
| ~ v1_funct_1(X303)
| ~ v1_relat_1(X303)
| X303 != k5_relset_2(X301,X302)
| k1_funct_1(X303,X304) = k9_relat_1(X302,X304)
| ~ r1_tarski(X304,X301) )
& ( ~ v1_relat_1(X302)
| ~ v1_funct_1(X303)
| ~ v1_relat_1(X303)
| X303 != k5_relset_2(X301,X302)
| k1_relat_1(X303) = k1_zfmisc_1(X301) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relset_2])])])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ v1_relat_1(k5_relset_2(esk1_0,esk3_0))
| m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_relat_1(k5_relset_2(esk1_0,esk3_0)),k1_zfmisc_1(k2_relat_1(esk3_0))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( ~ v1_relat_1(X2)
| v1_relat_1(k5_relset_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
v1_relat_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,plain,
( ~ v1_relat_1(X3)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| X1 != k5_relset_2(X2,X3)
| k1_relat_1(X1) = k1_zfmisc_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( ~ v1_relat_1(X2)
| v1_funct_1(k5_relset_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_45,plain,
! [X356,X357,X358] :
( m1_subset_1(X358,k1_zfmisc_1(k2_zfmisc_1(X356,X357)))
| ~ m2_relset_1(X358,X356,X357) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
cnf(c_0_46,negated_conjecture,
m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_relat_1(k5_relset_2(esk1_0,esk3_0)),k1_zfmisc_1(k2_relat_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_47,plain,
( ~ v1_relat_1(X2)
| k1_relat_1(k5_relset_2(X1,X2)) = k1_zfmisc_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_41]),c_0_44]) ).
fof(c_0_48,plain,
! [X123,X124] :
( ( ~ v1_relat_1(X123)
| ~ v1_relat_1(X124)
| ~ r1_tarski(X123,X124)
| r1_tarski(k2_relat_1(X123),k2_relat_1(X124)) )
& ( ~ v1_relat_1(X123)
| ~ v1_relat_1(X124)
| ~ r1_tarski(X123,X124)
| r1_tarski(k1_relat_1(X123),k1_relat_1(X124)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_relat_1])])])])]) ).
cnf(c_0_49,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,negated_conjecture,
m2_relset_1(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42])]) ).
cnf(c_0_51,plain,
np__1 = k1_tarski(np__0),
inference(split_conjunct,[status(thm)],[t1_card_5]) ).
cnf(c_0_52,plain,
np__0 = k1_xboole_0,
inference(split_conjunct,[status(thm)],[t51_card_1]) ).
cnf(c_0_53,plain,
( ~ v1_relat_1(X1)
| ~ v1_relat_1(X2)
| ~ r1_tarski(X1,X2)
| r1_tarski(k2_relat_1(X1),k2_relat_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
m1_subset_1(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))))),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
fof(c_0_55,plain,
! [X353,X354,X355] :
( v1_relat_1(X355)
| ~ m1_subset_1(X355,k1_zfmisc_1(k2_zfmisc_1(X353,X354))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
fof(c_0_56,plain,
! [X2794,X2795] : k1_zfmisc_1(k3_xboole_0(X2794,X2795)) = k3_xboole_0(k1_zfmisc_1(X2794),k1_zfmisc_1(X2795)),
inference(variable_rename,[status(thm)],[t83_zfmisc_1]) ).
cnf(c_0_57,plain,
k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0),
inference(split_conjunct,[status(thm)],[t1_zfmisc_1]) ).
cnf(c_0_58,plain,
k1_tarski(k1_xboole_0) = np__1,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_59,plain,
! [X2678] : k3_xboole_0(X2678,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_60,plain,
! [X1,X2] : k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(fof_simplification,[status(thm)],[t49_zfmisc_1]) ).
fof(c_0_61,plain,
! [X197,X198] :
( ( ~ v1_funct_1(X198)
| ~ v1_relat_1(X198)
| ~ r1_tarski(k2_relat_1(X198),X197)
| m2_relset_1(X198,k1_relat_1(X198),X197) )
& ( ~ v1_funct_1(X198)
| ~ v1_relat_1(X198)
| ~ r1_tarski(k2_relat_1(X198),X197)
| v1_funct_2(X198,k1_relat_1(X198),X197) )
& ( ~ v1_funct_1(X198)
| ~ v1_relat_1(X198)
| ~ r1_tarski(k2_relat_1(X198),X197)
| v1_funct_1(X198) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_funct_2])])])]) ).
cnf(c_0_62,plain,
( ~ r1_tarski(X1,X2)
| ~ v1_relat_1(X2)
| r1_tarski(k2_relat_1(X1),k2_relat_1(X2)) ),
inference(csr,[status(thm)],[c_0_53,c_0_36]) ).
cnf(c_0_63,negated_conjecture,
r1_tarski(k5_relset_2(esk1_0,esk3_0),k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0)))),
inference(spm,[status(thm)],[c_0_31,c_0_54]) ).
cnf(c_0_64,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_65,plain,
! [X2696,X2697] : k2_xboole_0(X2696,k3_xboole_0(X2696,X2697)) = X2696,
inference(variable_rename,[status(thm)],[t22_xboole_1]) ).
cnf(c_0_66,plain,
k1_zfmisc_1(k3_xboole_0(X1,X2)) = k3_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,plain,
k1_zfmisc_1(k1_xboole_0) = np__1,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_69,plain,
! [X1089,X1090] : k2_xboole_0(k1_tarski(X1089),X1090) != k1_xboole_0,
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_60])]) ).
cnf(c_0_70,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ r1_tarski(k2_relat_1(X1),X2)
| v1_funct_2(X1,k1_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,negated_conjecture,
r1_tarski(k2_relat_1(k5_relset_2(esk1_0,esk3_0)),k2_relat_1(k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_38])]) ).
cnf(c_0_72,negated_conjecture,
v1_relat_1(k5_relset_2(esk1_0,esk3_0)),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_73,plain,
k2_xboole_0(X1,k3_xboole_0(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
k3_xboole_0(k1_zfmisc_1(X1),np__1) = np__1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_67]) ).
fof(c_0_75,plain,
! [X1035,X1036] : k2_xboole_0(X1035,X1036) = k2_xboole_0(X1036,X1035),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_76,plain,
k2_xboole_0(k1_tarski(X1),X2) != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_77,plain,
! [X1038] : k2_xboole_0(X1038,k1_xboole_0) = X1038,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_78,negated_conjecture,
( ~ v1_funct_1(k5_relset_2(esk1_0,esk3_0))
| v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_relat_1(k5_relset_2(esk1_0,esk3_0)),k2_relat_1(k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
fof(c_0_79,plain,
! [X1,X2] :
~ ( ~ ( k2_relat_1(k2_zfmisc_1(X1,X2)) = X2
& k1_relat_1(k2_zfmisc_1(X1,X2)) = X1 )
& X2 != k1_xboole_0
& X1 != k1_xboole_0 ),
inference(fof_simplification,[status(thm)],[t12_sysrel]) ).
fof(c_0_80,plain,
! [X1071,X1072] :
( X1071 = k1_xboole_0
| k2_xboole_0(X1071,X1072) != k1_xboole_0 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t15_xboole_1])])]) ).
cnf(c_0_81,plain,
k2_xboole_0(k1_zfmisc_1(X1),np__1) = k1_zfmisc_1(X1),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
k2_xboole_0(np__1,X1) != k1_xboole_0,
inference(spm,[status(thm)],[c_0_76,c_0_58]) ).
cnf(c_0_84,plain,
k2_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_85,negated_conjecture,
v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_relat_1(k5_relset_2(esk1_0,esk3_0)),k2_relat_1(k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_44]),c_0_42])]) ).
fof(c_0_86,plain,
! [X254,X255] :
( ( X255 = k1_xboole_0
| X254 = k1_xboole_0
| k2_relat_1(k2_zfmisc_1(X254,X255)) = X255 )
& ( X255 = k1_xboole_0
| X254 = k1_xboole_0
| k1_relat_1(k2_zfmisc_1(X254,X255)) = X254 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])]) ).
cnf(c_0_87,plain,
( k2_xboole_0(X1,X2) != k1_xboole_0
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_88,plain,
k2_xboole_0(np__1,k1_zfmisc_1(X1)) = k1_zfmisc_1(X1),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_89,plain,
np__1 != k1_xboole_0,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( ~ 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_2(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(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_91,negated_conjecture,
v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k2_relat_1(k2_zfmisc_1(k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_47]),c_0_42])]) ).
cnf(c_0_92,plain,
( X2 = k1_xboole_0
| X1 = k1_xboole_0
| k2_relat_1(k2_zfmisc_1(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
k1_zfmisc_1(X1) != k1_xboole_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_94,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))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_50])]) ).
cnf(c_0_95,negated_conjecture,
v1_funct_2(k5_relset_2(esk1_0,esk3_0),k1_zfmisc_1(esk1_0),k1_zfmisc_1(k2_relat_1(esk3_0))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_93]) ).
cnf(c_0_96,negated_conjecture,
~ v1_funct_1(k5_relset_2(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_44]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU425+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n020.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 06:28:22 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/29.51 % Version: 3.5.1
% 0.26/29.51 % Preprocessing class: FMLLMLLLSSSNFFN.
% 0.26/29.51 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 0.26/29.51 % Starting new_bool_3 with 888s (3) cores
% 0.26/29.51 % Starting new_bool_1 with 888s (3) cores
% 0.26/29.51 % Starting sh5l with 296s (1) cores
% 0.26/29.51 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 296s (1) cores
% 0.26/29.51 % new_bool_1 with pid 2234537 completed with status 0
% 0.26/29.51 % Result found by new_bool_1
% 0.26/29.51 % Preprocessing class: FMLLMLLLSSSNFFN.
% 0.26/29.51 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 0.26/29.51 % Starting new_bool_3 with 888s (3) cores
% 0.26/29.51 % Starting new_bool_1 with 888s (3) cores
% 0.26/29.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/29.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/29.51 % Search class: FGHSM-SMLM32-MFFFFFNN
% 0.26/29.51 % Scheduled 13 strats onto 3 cores with 887 seconds (887 total)
% 0.26/29.51 % Starting SubtermCWHack with 80s (1) cores
% 0.26/29.51 % Starting new_bool_1 with 89s (1) cores
% 0.26/29.51 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 67s (1) cores
% 0.26/29.51 % new_bool_1 with pid 2234545 completed with status 0
% 0.26/29.51 % Result found by new_bool_1
% 0.26/29.51 % Preprocessing class: FMLLMLLLSSSNFFN.
% 0.26/29.51 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 0.26/29.51 % Starting new_bool_3 with 888s (3) cores
% 0.26/29.51 % Starting new_bool_1 with 888s (3) cores
% 0.26/29.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/29.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/29.51 % Search class: FGHSM-SMLM32-MFFFFFNN
% 0.26/29.51 % Scheduled 13 strats onto 3 cores with 887 seconds (887 total)
% 0.26/29.51 % Starting SubtermCWHack with 80s (1) cores
% 0.26/29.51 % Starting new_bool_1 with 89s (1) cores
% 0.26/29.51 % Preprocessing time : 0.275 s
% 0.26/29.51 % Presaturation interreduction done
% 0.26/29.51
% 0.26/29.51 % Proof found!
% 0.26/29.51 % SZS status Theorem
% 0.26/29.51 % SZS output start CNFRefutation
% See solution above
% 0.26/29.51 % Parsed axioms : 71102
% 0.26/29.51 % Removed by relevancy pruning/SinE : 69471
% 0.26/29.51 % Initial clauses : 3413
% 0.26/29.51 % Removed in clause preprocessing : 56
% 0.26/29.51 % Initial clauses in saturation : 3357
% 0.26/29.51 % Processed clauses : 47689
% 0.26/29.51 % ...of these trivial : 965
% 0.26/29.51 % ...subsumed : 30679
% 0.26/29.51 % ...remaining for further processing : 16045
% 0.26/29.51 % Other redundant clauses eliminated : 3676
% 0.26/29.51 % Clauses deleted for lack of memory : 0
% 0.26/29.51 % Backward-subsumed : 330
% 0.26/29.51 % Backward-rewritten : 369
% 0.26/29.51 % Generated clauses : 603375
% 0.26/29.51 % ...of the previous two non-redundant : 529432
% 0.26/29.51 % ...aggressively subsumed : 0
% 0.26/29.51 % Contextual simplify-reflections : 256
% 0.26/29.51 % Paramodulations : 599591
% 0.26/29.51 % Factorizations : 36
% 0.26/29.51 % NegExts : 0
% 0.26/29.51 % Equation resolutions : 3796
% 0.26/29.51 % Disequality decompositions : 0
% 0.26/29.51 % Total rewrite steps : 411213
% 0.26/29.51 % ...of those cached : 334346
% 0.26/29.51 % Propositional unsat checks : 3
% 0.26/29.51 % Propositional check models : 1
% 0.26/29.51 % Propositional check unsatisfiable : 0
% 0.26/29.51 % Propositional clauses : 0
% 0.26/29.51 % Propositional clauses after purity: 0
% 0.26/29.51 % Propositional unsat core size : 0
% 0.26/29.51 % Propositional preprocessing time : 0.000
% 0.26/29.51 % Propositional encoding time : 0.792
% 0.26/29.51 % Propositional solver time : 0.579
% 0.26/29.51 % Success case prop preproc time : 0.000
% 0.26/29.51 % Success case prop encoding time : 0.000
% 0.26/29.51 % Success case prop solver time : 0.000
% 0.26/29.51 % Current number of processed clauses : 12037
% 0.26/29.51 % Positive orientable unit clauses : 3260
% 0.26/29.51 % Positive unorientable unit clauses: 7
% 0.26/29.51 % Negative unit clauses : 2633
% 0.26/29.51 % Non-unit-clauses : 6137
% 0.26/29.51 % Current number of unprocessed clauses: 487252
% 0.26/29.51 % ...number of literals in the above : 1163698
% 0.26/29.51 % Current number of archived formulas : 0
% 0.26/29.51 % Current number of archived clauses : 3725
% 0.26/29.51 % Clause-clause subsumption calls (NU) : 17171257
% 0.26/29.51 % Rec. Clause-clause subsumption calls : 3473431
% 0.26/29.51 % Non-unit clause-clause subsumptions : 7982
% 0.26/29.51 % Unit Clause-clause subsumption calls : 3902750
% 0.26/29.51 % Rewrite failures with RHS unbound : 0
% 0.26/29.51 % BW rewrite match attempts : 6888
% 0.26/29.51 % BW rewrite match successes : 486
% 0.26/29.51 % Condensation attempts : 0
% 0.26/29.51 % Condensation successes : 0
% 0.26/29.51 % Termbank termtop insertions : 14163611
% 0.26/29.51 % Search garbage collected termcells : 825040
% 0.26/29.51
% 0.26/29.51 % -------------------------------------------------
% 0.26/29.51 % User time : 22.635 s
% 0.26/29.51 % System time : 0.874 s
% 0.26/29.51 % Total time : 23.509 s
% 0.26/29.51 % Maximum resident set size: 149268 pages
% 0.26/29.51
% 0.26/29.51 % -------------------------------------------------
% 0.26/29.51 % User time : 69.611 s
% 0.26/29.51 % System time : 2.075 s
% 0.26/29.51 % Total time : 71.686 s
% 0.26/29.51 % Maximum resident set size: 121088 pages
% 0.26/29.51 % E exiting
%------------------------------------------------------------------------------