%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU448+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:25:14 PM UTC 2026
% Result : Theorem 8.78s 2.34s
% Output : CNFRefutation 8.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 101 ( 29 unt; 0 def)
% Number of atoms : 238 ( 14 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 228 ( 91 ~; 98 |; 9 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 164 ( 6 sgn 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t62_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> ( r1_tarski(k10_relset_1(X1,X2,X5,k3_subset_1(X1,X3)),k3_subset_1(X2,X4))
<=> r1_tarski(k10_relset_1(X2,X1,k6_relset_1(X1,X2,X5),X4),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_relset_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
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(fc1_subset_1,axiom,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(redefinition_k6_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> k6_relset_1(X1,X2,X3) = k4_relat_1(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( r2_hidden(X1,X2)
| v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(redefinition_k10_relset_1,axiom,
! [X1,X2,X3,X4] :
( m1_relset_1(X3,X1,X2)
=> k10_relset_1(X1,X2,X3,X4) = k9_relat_1(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
fof(dt_k10_relset_1,axiom,
! [X1,X2,X3,X4] :
( m1_relset_1(X3,X1,X2)
=> m1_subset_1(k10_relset_1(X1,X2,X3,X4),k1_zfmisc_1(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relset_1) ).
fof(dt_k6_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> m2_relset_1(k6_relset_1(X1,X2,X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(t43_subset_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_xboole_0(X2,X3)
<=> r1_tarski(X2,k3_subset_1(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( r1_xboole_0(X1,X2)
=> r1_xboole_0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t46_relset_2,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( r1_xboole_0(X3,k9_relat_1(k4_relat_1(X5),X4))
<=> r1_xboole_0(X4,k9_relat_1(X5,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relset_2) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(k3_subset_1(X1,X2),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
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/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> k3_subset_1(X1,k3_subset_1(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(t44_subset_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ( r1_xboole_0(X2,k3_subset_1(X1,X3))
<=> r1_tarski(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_subset_1) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> ( r1_tarski(k10_relset_1(X1,X2,X5,k3_subset_1(X1,X3)),k3_subset_1(X2,X4))
<=> r1_tarski(k10_relset_1(X2,X1,k6_relset_1(X1,X2,X5),X4),X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t62_relset_2]) ).
fof(c_0_18,plain,
! [X74,X75] :
( ( m1_subset_1(X74,k1_zfmisc_1(X75))
| ~ r1_tarski(X74,X75) )
& ( r1_tarski(X74,X75)
| ~ m1_subset_1(X74,k1_zfmisc_1(X75)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
fof(c_0_19,negated_conjecture,
( ( r1_tarski(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),esk3_0)
| r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) )
& ( ~ r1_tarski(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),esk3_0)
| ~ r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) )
& m2_relset_1(esk5_0,esk1_0,esk2_0)
& m1_subset_1(esk4_0,k1_zfmisc_1(esk2_0))
& m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_20,plain,
! [X64,X65,X66] :
( ( m2_relset_1(X66,X64,X65)
| ~ m1_relset_1(X66,X64,X65) )
& ( m1_relset_1(X66,X64,X65)
| ~ m2_relset_1(X66,X64,X65) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_21,plain,
( ~ r1_tarski(X1,X2)
| m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( r1_tarski(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),esk3_0)
| r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X1] : ~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_24,plain,
! [X61,X62,X63] :
( k6_relset_1(X61,X62,X63) = k4_relat_1(X63)
| ~ m1_relset_1(X63,X61,X62) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_relset_1])])]) ).
cnf(c_0_25,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
m2_relset_1(esk5_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X72,X73] :
( r2_hidden(X72,X73)
| v1_xboole_0(X73)
| ~ m1_subset_1(X72,X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_28,negated_conjecture,
( m1_subset_1(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k1_zfmisc_1(k3_subset_1(esk2_0,esk4_0)))
| r1_tarski(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X39] : ~ v1_xboole_0(k1_zfmisc_1(X39)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
cnf(c_0_30,plain,
( ~ m1_relset_1(X1,X2,X3)
| k6_relset_1(X2,X3,X1) = k4_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
m1_relset_1(esk5_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_32,plain,
! [X70,X71] :
( m1_subset_1(X70,X71)
| ~ r2_hidden(X70,X71) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_33,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| m1_subset_1(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k1_zfmisc_1(k3_subset_1(esk2_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_35,plain,
~ v1_xboole_0(k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
k6_relset_1(esk1_0,esk2_0,esk5_0) = k4_relat_1(esk5_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r2_hidden(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k1_zfmisc_1(k3_subset_1(esk2_0,esk4_0))) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).
fof(c_0_39,plain,
! [X57,X58,X59,X60] :
( k10_relset_1(X57,X58,X59,X60) = k9_relat_1(X59,X60)
| ~ m1_relset_1(X59,X57,X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k10_relset_1])])]) ).
fof(c_0_40,plain,
! [X17,X18,X19,X20] :
( m1_subset_1(k10_relset_1(X17,X18,X19,X20),k1_zfmisc_1(X18))
| ~ m1_relset_1(X19,X17,X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k10_relset_1])])]) ).
cnf(c_0_41,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| m1_subset_1(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k1_zfmisc_1(k3_subset_1(esk2_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( ~ m1_relset_1(X1,X2,X3)
| k10_relset_1(X2,X3,X1,X4) = k9_relat_1(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( ~ m1_relset_1(X1,X2,X3)
| m1_subset_1(k10_relset_1(X2,X3,X1,X4),k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_45,plain,
! [X24,X25,X26] :
( m2_relset_1(k6_relset_1(X24,X25,X26),X25,X24)
| ~ m1_relset_1(X26,X24,X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_relset_1])])]) ).
fof(c_0_46,plain,
! [X76,X77,X78] :
( ( ~ m1_subset_1(X77,k1_zfmisc_1(X76))
| ~ m1_subset_1(X78,k1_zfmisc_1(X76))
| r1_xboole_0(X77,X78)
| ~ r1_tarski(X77,k3_subset_1(X76,X78)) )
& ( ~ m1_subset_1(X77,k1_zfmisc_1(X76))
| ~ m1_subset_1(X78,k1_zfmisc_1(X76))
| r1_tarski(X77,k3_subset_1(X76,X78))
| ~ r1_xboole_0(X77,X78) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_subset_1])])])])]) ).
cnf(c_0_47,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
k10_relset_1(esk1_0,esk2_0,esk5_0,X1) = k9_relat_1(esk5_0,X1),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_49,negated_conjecture,
m1_subset_1(k10_relset_1(esk1_0,esk2_0,esk5_0,X1),k1_zfmisc_1(esk2_0)),
inference(spm,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_50,plain,
( ~ m1_relset_1(X1,X2,X3)
| m2_relset_1(k6_relset_1(X2,X3,X1),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_51,plain,
! [X68,X69] :
( r1_xboole_0(X69,X68)
| ~ r1_xboole_0(X68,X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
cnf(c_0_52,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,k3_subset_1(X2,X3))
| r1_xboole_0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_tarski(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_55,negated_conjecture,
m1_subset_1(k9_relat_1(esk5_0,X1),k1_zfmisc_1(esk2_0)),
inference(rw,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
m2_relset_1(k4_relat_1(esk5_0),esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_31]),c_0_36]) ).
cnf(c_0_57,plain,
( ~ r1_xboole_0(X1,X2)
| r1_xboole_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55])]) ).
cnf(c_0_59,negated_conjecture,
m1_relset_1(k4_relat_1(esk5_0),esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_25,c_0_56]) ).
fof(c_0_60,plain,
! [X82,X83,X84,X85,X86] :
( ( ~ m1_subset_1(X84,k1_zfmisc_1(X82))
| ~ m1_subset_1(X85,k1_zfmisc_1(X83))
| ~ m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))
| r1_xboole_0(X84,k9_relat_1(k4_relat_1(X86),X85))
| ~ r1_xboole_0(X85,k9_relat_1(X86,X84)) )
& ( ~ m1_subset_1(X84,k1_zfmisc_1(X82))
| ~ m1_subset_1(X85,k1_zfmisc_1(X83))
| ~ m1_subset_1(X86,k1_zfmisc_1(k2_zfmisc_1(X82,X83)))
| r1_xboole_0(X85,k9_relat_1(X86,X84))
| ~ r1_xboole_0(X84,k9_relat_1(k4_relat_1(X86),X85)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_relset_2])])])])]) ).
cnf(c_0_61,negated_conjecture,
( m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(esk4_0,k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),X1) = k9_relat_1(k4_relat_1(esk5_0),X1),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
cnf(c_0_63,plain,
( ~ m1_subset_1(X3,k1_zfmisc_1(X4))
| ~ m1_subset_1(X1,k1_zfmisc_1(X5))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ r1_xboole_0(X1,k9_relat_1(X2,X3))
| r1_xboole_0(X3,k9_relat_1(k4_relat_1(X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(esk4_0,k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0))) ),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_65,plain,
! [X21,X22] :
( m1_subset_1(k3_subset_1(X21,X22),k1_zfmisc_1(X21))
| ~ m1_subset_1(X22,k1_zfmisc_1(X21)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])])]) ).
fof(c_0_66,plain,
! [X27,X28,X29] :
( m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28)))
| ~ m2_relset_1(X29,X27,X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
cnf(c_0_67,negated_conjecture,
( ~ m1_subset_1(esk4_0,k1_zfmisc_1(X2))
| ~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_subset_1(k3_subset_1(esk1_0,esk3_0),k1_zfmisc_1(X1))
| m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(k3_subset_1(esk1_0,esk3_0),k9_relat_1(k4_relat_1(esk5_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(k3_subset_1(X2,X1),k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_69,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_70,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_66]) ).
fof(c_0_71,plain,
! [X44,X45] :
( k3_subset_1(X44,k3_subset_1(X44,X45)) = X45
| ~ m1_subset_1(X45,k1_zfmisc_1(X44)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])]) ).
cnf(c_0_72,negated_conjecture,
( ~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(X1,esk2_0)))
| ~ m1_subset_1(k3_subset_1(esk1_0,esk3_0),k1_zfmisc_1(X1))
| m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(k3_subset_1(esk1_0,esk3_0),k9_relat_1(k4_relat_1(esk5_0),esk4_0)) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_73,negated_conjecture,
m1_subset_1(k3_subset_1(esk1_0,esk3_0),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_70,c_0_26]) ).
cnf(c_0_75,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| k3_subset_1(X2,k3_subset_1(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_76,plain,
! [X79,X80,X81] :
( ( ~ m1_subset_1(X80,k1_zfmisc_1(X79))
| ~ m1_subset_1(X81,k1_zfmisc_1(X79))
| r1_xboole_0(X80,k3_subset_1(X79,X81))
| ~ r1_tarski(X80,X81) )
& ( ~ m1_subset_1(X80,k1_zfmisc_1(X79))
| ~ m1_subset_1(X81,k1_zfmisc_1(X79))
| r1_tarski(X80,X81)
| ~ r1_xboole_0(X80,k3_subset_1(X79,X81)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_subset_1])])])])]) ).
cnf(c_0_77,negated_conjecture,
( m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(k3_subset_1(esk1_0,esk3_0),k9_relat_1(k4_relat_1(esk5_0),esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]) ).
cnf(c_0_78,negated_conjecture,
m1_subset_1(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),X1),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_44,c_0_59]) ).
cnf(c_0_79,negated_conjecture,
k3_subset_1(esk1_0,k3_subset_1(esk1_0,esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_75,c_0_69]) ).
cnf(c_0_80,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ r1_xboole_0(X1,k3_subset_1(X2,X3))
| r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k1_zfmisc_1(esk3_0))
| r1_xboole_0(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k3_subset_1(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_77]) ).
cnf(c_0_82,negated_conjecture,
m1_subset_1(k9_relat_1(k4_relat_1(esk5_0),X1),k1_zfmisc_1(esk1_0)),
inference(rw,[status(thm)],[c_0_78,c_0_62]) ).
cnf(c_0_83,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(esk1_0))
| ~ r1_tarski(X1,esk3_0)
| r1_xboole_0(X1,k3_subset_1(esk1_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_79]),c_0_73])]) ).
cnf(c_0_84,negated_conjecture,
r1_tarski(k9_relat_1(k4_relat_1(esk5_0),esk4_0),esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_69]),c_0_82])]),c_0_41]) ).
cnf(c_0_85,negated_conjecture,
r1_xboole_0(k9_relat_1(k4_relat_1(esk5_0),esk4_0),k3_subset_1(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_82])]) ).
cnf(c_0_86,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(X5))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ r1_xboole_0(X1,k9_relat_1(k4_relat_1(X2),X3))
| r1_xboole_0(X3,k9_relat_1(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_87,negated_conjecture,
r1_xboole_0(k3_subset_1(esk1_0,esk3_0),k9_relat_1(k4_relat_1(esk5_0),esk4_0)),
inference(spm,[status(thm)],[c_0_57,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( ~ r1_tarski(k10_relset_1(esk2_0,esk1_0,k6_relset_1(esk1_0,esk2_0,esk5_0),esk4_0),esk3_0)
| ~ r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_89,negated_conjecture,
( ~ m1_subset_1(esk4_0,k1_zfmisc_1(X2))
| ~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m1_subset_1(k3_subset_1(esk1_0,esk3_0),k1_zfmisc_1(X1))
| r1_xboole_0(esk4_0,k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0))) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,negated_conjecture,
( ~ r1_tarski(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),esk3_0)
| ~ r1_tarski(k10_relset_1(esk1_0,esk2_0,esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_36]) ).
cnf(c_0_91,negated_conjecture,
( ~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(X1,esk2_0)))
| ~ m1_subset_1(k3_subset_1(esk1_0,esk3_0),k1_zfmisc_1(X1))
| r1_xboole_0(esk4_0,k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0))) ),
inference(spm,[status(thm)],[c_0_89,c_0_54]) ).
cnf(c_0_92,negated_conjecture,
( ~ r1_tarski(k10_relset_1(esk2_0,esk1_0,k4_relat_1(esk5_0),esk4_0),esk3_0)
| ~ r1_tarski(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_90,c_0_48]) ).
cnf(c_0_93,negated_conjecture,
k3_subset_1(esk2_0,k3_subset_1(esk2_0,esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_75,c_0_54]) ).
cnf(c_0_94,negated_conjecture,
m1_subset_1(k3_subset_1(esk2_0,esk4_0),k1_zfmisc_1(esk2_0)),
inference(spm,[status(thm)],[c_0_68,c_0_54]) ).
cnf(c_0_95,negated_conjecture,
r1_xboole_0(esk4_0,k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_73]),c_0_74])]) ).
cnf(c_0_96,negated_conjecture,
( ~ r1_tarski(k9_relat_1(k4_relat_1(esk5_0),esk4_0),esk3_0)
| ~ r1_tarski(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)) ),
inference(rw,[status(thm)],[c_0_92,c_0_62]) ).
cnf(c_0_97,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(esk2_0))
| ~ r1_xboole_0(X1,esk4_0)
| r1_tarski(X1,k3_subset_1(esk2_0,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_93]),c_0_94])]) ).
cnf(c_0_98,negated_conjecture,
r1_xboole_0(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),esk4_0),
inference(spm,[status(thm)],[c_0_57,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
~ r1_tarski(k9_relat_1(esk5_0,k3_subset_1(esk1_0,esk3_0)),k3_subset_1(esk2_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_84])]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_55])]),c_0_99]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU448+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 06:34:25 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.53 Running first-order theorem proving
% 0.27/0.53 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 8.78/2.34 % Version: 3.5.1
% 8.78/2.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.78/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.78/2.34 % Starting new_bool_3 with 300s (1) cores
% 8.78/2.34 % Starting new_bool_1 with 300s (1) cores
% 8.78/2.34 % Starting sh5l with 300s (1) cores
% 8.78/2.34 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1215723 completed with status 0
% 8.78/2.34 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 8.78/2.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.78/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.78/2.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.78/2.34 % No SInE strategy applied
% 8.78/2.34 % Search class: FGHSM-FFMM31-SFFFFFNN
% 8.78/2.34 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 8.78/2.34 % Starting SubtermCWHack with 136s (1) cores
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 8.78/2.34 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 8.78/2.34 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.78/2.34 % G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 1215729 completed with status 0
% 8.78/2.34 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 8.78/2.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 8.78/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.78/2.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.78/2.34 % No SInE strategy applied
% 8.78/2.34 % Search class: FGHSM-FFMM31-SFFFFFNN
% 8.78/2.34 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 8.78/2.34 % Starting SubtermCWHack with 136s (1) cores
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 8.78/2.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 8.78/2.34 % Preprocessing time : 0.003 s
% 8.78/2.34 % Presaturation interreduction done
% 8.78/2.34
% 8.78/2.34 % Proof found!
% 8.78/2.34 % SZS status Theorem
% 8.78/2.34 % SZS output start CNFRefutation
% See solution above
% 8.78/2.34 % Parsed axioms : 48
% 8.78/2.34 % Removed by relevancy pruning/SinE : 0
% 8.78/2.34 % Initial clauses : 66
% 8.78/2.34 % Removed in clause preprocessing : 6
% 8.78/2.34 % Initial clauses in saturation : 60
% 8.78/2.34 % Processed clauses : 7190
% 8.78/2.34 % ...of these trivial : 938
% 8.78/2.34 % ...subsumed : 2946
% 8.78/2.34 % ...remaining for further processing : 3306
% 8.78/2.34 % Other redundant clauses eliminated : 0
% 8.78/2.34 % Clauses deleted for lack of memory : 0
% 8.78/2.34 % Backward-subsumed : 63
% 8.78/2.34 % Backward-rewritten : 1337
% 8.78/2.34 % Generated clauses : 29495
% 8.78/2.34 % ...of the previous two non-redundant : 26080
% 8.78/2.34 % ...aggressively subsumed : 0
% 8.78/2.34 % Contextual simplify-reflections : 10
% 8.78/2.34 % Paramodulations : 29494
% 8.78/2.34 % Factorizations : 0
% 8.78/2.34 % NegExts : 0
% 8.78/2.34 % Equation resolutions : 0
% 8.78/2.34 % Disequality decompositions : 0
% 8.78/2.34 % Total rewrite steps : 35484
% 8.78/2.34 % ...of those cached : 33395
% 8.78/2.34 % Propositional unsat checks : 0
% 8.78/2.34 % Propositional check models : 0
% 8.78/2.34 % Propositional check unsatisfiable : 0
% 8.78/2.34 % Propositional clauses : 0
% 8.78/2.34 % Propositional clauses after purity: 0
% 8.78/2.34 % Propositional unsat core size : 0
% 8.78/2.34 % Propositional preprocessing time : 0.000
% 8.78/2.34 % Propositional encoding time : 0.000
% 8.78/2.34 % Propositional solver time : 0.000
% 8.78/2.34 % Success case prop preproc time : 0.000
% 8.78/2.34 % Success case prop encoding time : 0.000
% 8.78/2.34 % Success case prop solver time : 0.000
% 8.78/2.34 % Current number of processed clauses : 1847
% 8.78/2.34 % Positive orientable unit clauses : 660
% 8.78/2.34 % Positive unorientable unit clauses: 0
% 8.78/2.34 % Negative unit clauses : 109
% 8.78/2.34 % Non-unit-clauses : 1078
% 8.78/2.34 % Current number of unprocessed clauses: 16460
% 8.78/2.34 % ...number of literals in the above : 37328
% 8.78/2.34 % Current number of archived formulas : 0
% 8.78/2.34 % Current number of archived clauses : 1459
% 8.78/2.34 % Clause-clause subsumption calls (NU) : 221077
% 8.78/2.34 % Rec. Clause-clause subsumption calls : 191518
% 8.78/2.34 % Non-unit clause-clause subsumptions : 2592
% 8.78/2.34 % Unit Clause-clause subsumption calls : 64447
% 8.78/2.34 % Rewrite failures with RHS unbound : 0
% 8.78/2.34 % BW rewrite match attempts : 7648
% 8.78/2.34 % BW rewrite match successes : 256
% 8.78/2.34 % Condensation attempts : 0
% 8.78/2.34 % Condensation successes : 0
% 8.78/2.34 % Termbank termtop insertions : 841284
% 8.78/2.34 % Search garbage collected termcells : 658
% 8.78/2.34
% 8.78/2.34 % -------------------------------------------------
% 8.78/2.34 % User time : 1.641 s
% 8.78/2.34 % System time : 0.067 s
% 8.78/2.34 % Total time : 1.709 s
% 8.78/2.34 % Maximum resident set size: 3672 pages
% 8.78/2.34
% 8.78/2.34 % -------------------------------------------------
% 8.78/2.34 % User time : 8.233 s
% 8.78/2.34 % System time : 0.231 s
% 8.78/2.34 % Total time : 8.464 s
% 8.78/2.34 % Maximum resident set size: 4608 pages
% 8.78/2.34 % E exiting
%------------------------------------------------------------------------------