%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG225+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 : n007.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 12:01:42 PM UTC 2026
% Result : Theorem 271.44s 35.78s
% Output : CNFRefutation 271.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 95 ( 28 unt; 0 def)
% Number of atoms : 281 ( 64 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 297 ( 111 ~; 123 |; 29 &)
% ( 8 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 5 sgn 83 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fraenkel_a_2_0_closure3,axiom,
! [X1,X2,X3] :
( ( m1_pboole(X3,X2)
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( k1_funct_1(X3,X4) != k1_xboole_0
& X1 = X4
& m1_subset_1(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(t6_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_closure3) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( r1_tarski(X1,X2)
<=> ! [X3] :
( r2_hidden(X3,X1)
=> r2_hidden(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(d3_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
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(d3_pboole,axiom,
! [X1,X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( m1_pboole(X2,X1)
<=> k1_relat_1(X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pboole) ).
fof(dt_m1_pboole,axiom,
! [X1,X2] :
( m1_pboole(X2,X1)
=> ( v1_funct_1(X2)
& v1_relat_1(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(d16_pboole,axiom,
! [X1,X2] :
( m1_pboole(X2,X1)
=> ( v2_relat_1(X2)
<=> ! [X3] :
~ ( v1_xboole_0(k1_funct_1(X2,X3))
& r2_hidden(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_pboole) ).
fof(t1_closure3,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_pboole(X3,X1)
=> k1_funct_4(X2,X3) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_closure3) ).
fof(d6_pboole,axiom,
! [X1] : k1_pboole(X1) = k2_funcop_1(X1,k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pboole) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( r1_tarski(X2,X1)
& r1_tarski(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(t97_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(k1_relat_1(X2),X1)
=> k7_relat_1(X2,X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_relat_1) ).
fof(dt_k1_pboole,axiom,
! [X1] : m1_pboole(k1_pboole(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_pboole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( ( m1_pboole(X3,X2)
& ~ v1_xboole_0(X2) )
=> ( r2_hidden(X1,a_2_0_closure3(X2,X3))
<=> ? [X4] :
( k1_funct_1(X3,X4) != k1_xboole_0
& X1 = X4
& m1_subset_1(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_closure3]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
inference(assume_negation,[status(cth)],[t6_closure3]) ).
fof(c_0_19,plain,
! [X58,X59,X60,X62] :
( ( ~ m1_pboole(X60,X59)
| v1_xboole_0(X59)
| r2_hidden(X58,a_2_0_closure3(X59,X60))
| k1_funct_1(X60,X62) = k1_xboole_0
| X58 != X62
| ~ m1_subset_1(X62,X59) )
& ( ~ m1_pboole(X60,X59)
| v1_xboole_0(X59)
| ~ r2_hidden(X58,a_2_0_closure3(X59,X60))
| k1_funct_1(X60,esk7_3(X58,X59,X60)) != k1_xboole_0 )
& ( ~ m1_pboole(X60,X59)
| v1_xboole_0(X59)
| ~ r2_hidden(X58,a_2_0_closure3(X59,X60))
| X58 = esk7_3(X58,X59,X60) )
& ( ~ m1_pboole(X60,X59)
| v1_xboole_0(X59)
| ~ r2_hidden(X58,a_2_0_closure3(X59,X60))
| m1_subset_1(esk7_3(X58,X59,X60),X59) ) ),
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)],[c_0_17])])])])])]) ).
fof(c_0_20,plain,
! [X32,X33,X34,X35,X36] :
( ( r1_tarski(X35,X36)
| ~ r2_hidden(esk4_2(X35,X36),X36) )
& ( r1_tarski(X35,X36)
| r2_hidden(esk4_2(X35,X36),X35) )
& ( r2_hidden(X34,X33)
| ~ r2_hidden(X34,X32)
| ~ r1_tarski(X32,X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> X2 = k1_funct_4(k1_pboole(X1),k7_relat_1(X2,k1_closure3(X1,X2))) ) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X96,X97] :
( m1_subset_1(X96,X97)
| ~ r2_hidden(X96,X97) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
fof(c_0_23,plain,
! [X112,X113] :
( ~ v1_xboole_0(X113)
| ~ r2_hidden(X112,X113) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_24,plain,
( ~ m1_pboole(X3,X2)
| ~ r2_hidden(X1,a_2_0_closure3(X2,X3))
| v1_xboole_0(X2)
| m1_subset_1(esk7_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( r1_tarski(X1,X2)
| r2_hidden(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,negated_conjecture,
( esk2_0 != k1_funct_4(k1_pboole(esk1_0),k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)))
& m1_pboole(esk2_0,esk1_0)
& v2_relat_1(esk2_0)
& ~ v1_xboole_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_27,plain,
( ~ m1_pboole(X3,X2)
| ~ r2_hidden(X1,a_2_0_closure3(X2,X3))
| v1_xboole_0(X2)
| X1 = esk7_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ m1_pboole(X4,X2)
| X3 != X1
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X3,a_2_0_closure3(X2,X4))
| k1_funct_1(X4,X1) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| m1_subset_1(esk7_3(esk4_2(a_2_0_closure3(X1,X2),X3),X1,X2),X1)
| r1_tarski(a_2_0_closure3(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| r1_tarski(a_2_0_closure3(X1,X2),X3)
| esk7_3(esk4_2(a_2_0_closure3(X1,X2),X3),X1,X2) = esk4_2(a_2_0_closure3(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_35,plain,
( ~ m1_pboole(X1,X3)
| ~ m1_subset_1(X2,X3)
| v1_xboole_0(X3)
| r2_hidden(X2,a_2_0_closure3(X3,X1))
| k1_funct_1(X1,X2) = k1_xboole_0 ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( m1_subset_1(esk4_2(X1,X2),X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_37,plain,
( ~ v1_xboole_0(X1)
| r1_tarski(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
fof(c_0_38,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( X3 = k1_closure3(X1,X2)
<=> X3 = a_2_0_closure3(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d3_closure3]) ).
fof(c_0_39,plain,
! [X98,X99] :
( r2_hidden(X98,X99)
| v1_xboole_0(X99)
| ~ m1_subset_1(X98,X99) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
cnf(c_0_40,negated_conjecture,
( m1_subset_1(esk7_3(esk4_2(a_2_0_closure3(esk1_0,esk2_0),X1),esk1_0,esk2_0),esk1_0)
| r1_tarski(a_2_0_closure3(esk1_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( r1_tarski(a_2_0_closure3(esk1_0,esk2_0),X1)
| esk7_3(esk4_2(a_2_0_closure3(esk1_0,esk2_0),X1),esk1_0,esk2_0) = esk4_2(a_2_0_closure3(esk1_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_33]) ).
cnf(c_0_42,plain,
( ~ m1_pboole(X1,X2)
| r2_hidden(esk4_2(X2,X3),a_2_0_closure3(X2,X1))
| r1_tarski(X2,X3)
| k1_funct_1(X1,esk4_2(X2,X3)) = k1_xboole_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
fof(c_0_43,plain,
! [X30,X31] :
( ( ~ v1_funct_1(X31)
| ~ v1_relat_1(X31)
| m1_pboole(X31,X30)
| k1_relat_1(X31) != X30 )
& ( ~ v1_funct_1(X31)
| ~ v1_relat_1(X31)
| k1_relat_1(X31) = X30
| ~ m1_pboole(X31,X30) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pboole])])])]) ).
fof(c_0_44,plain,
! [X44,X45] :
( ( ~ m1_pboole(X45,X44)
| v1_funct_1(X45) )
& ( ~ m1_pboole(X45,X44)
| v1_relat_1(X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_pboole])])])]) ).
fof(c_0_45,plain,
! [X27,X28,X29] :
( ( v1_xboole_0(X27)
| ~ m1_pboole(X28,X27)
| X29 = k1_closure3(X27,X28)
| X29 != a_2_0_closure3(X27,X28) )
& ( v1_xboole_0(X27)
| ~ m1_pboole(X28,X27)
| X29 = a_2_0_closure3(X27,X28)
| X29 != k1_closure3(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])]) ).
cnf(c_0_46,plain,
( ~ m1_subset_1(X1,X2)
| r2_hidden(X1,X2)
| v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( m1_subset_1(esk4_2(a_2_0_closure3(esk1_0,esk2_0),X1),esk1_0)
| r1_tarski(a_2_0_closure3(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_48,plain,
! [X23,X24,X25] :
( ( ~ m1_pboole(X24,X23)
| v2_relat_1(X24)
| v1_xboole_0(k1_funct_1(X24,esk3_2(X23,X24))) )
& ( ~ m1_pboole(X24,X23)
| v2_relat_1(X24)
| r2_hidden(esk3_2(X23,X24),X23) )
& ( ~ m1_pboole(X24,X23)
| ~ v1_xboole_0(k1_funct_1(X24,X25))
| ~ r2_hidden(X25,X23)
| ~ v2_relat_1(X24) ) ),
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)],[d16_pboole])])])])])]) ).
cnf(c_0_49,plain,
( ~ r2_hidden(esk4_2(X1,X2),X2)
| r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_50,negated_conjecture,
( r2_hidden(esk4_2(esk1_0,X1),a_2_0_closure3(esk1_0,esk2_0))
| r1_tarski(esk1_0,X1)
| k1_funct_1(esk2_0,esk4_2(esk1_0,X1)) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_51,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ m1_pboole(X1,X2)
| k1_relat_1(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( ~ m1_pboole(X1,X2)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( ~ m1_pboole(X1,X2)
| v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_pboole(X2,X1)
=> ! [X3] :
( m1_pboole(X3,X1)
=> k1_funct_4(X2,X3) = X3 ) ) ),
inference(fof_simplification,[status(thm)],[t1_closure3]) ).
fof(c_0_55,plain,
! [X38] : k1_pboole(X38) = k2_funcop_1(X38,k1_xboole_0),
inference(variable_rename,[status(thm)],[d6_pboole]) ).
cnf(c_0_56,plain,
( ~ m1_pboole(X3,X2)
| X1 != k1_closure3(X2,X3)
| v1_xboole_0(X2)
| X1 = a_2_0_closure3(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_57,plain,
! [X21,X22] :
( ( X21 = X22
| ~ r1_tarski(X22,X21)
| ~ r1_tarski(X21,X22) )
& ( X21 != X22
| r1_tarski(X22,X21) )
& ( X21 != X22
| r1_tarski(X21,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])]) ).
cnf(c_0_58,negated_conjecture,
( r2_hidden(esk4_2(a_2_0_closure3(esk1_0,esk2_0),X1),esk1_0)
| r1_tarski(a_2_0_closure3(esk1_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_33]) ).
cnf(c_0_59,plain,
( ~ m1_pboole(X1,X3)
| ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ r2_hidden(X2,X3)
| ~ v2_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( r1_tarski(esk1_0,a_2_0_closure3(esk1_0,esk2_0))
| k1_funct_1(esk2_0,esk4_2(esk1_0,a_2_0_closure3(esk1_0,esk2_0))) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_61,negated_conjecture,
v2_relat_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_62,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_63,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_relat_1(X1) != X2
| m1_pboole(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_64,plain,
( ~ m1_pboole(X1,X2)
| k1_relat_1(X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
fof(c_0_65,plain,
! [X116,X117] :
( k7_relat_1(X117,X116) = X117
| ~ r1_tarski(k1_relat_1(X117),X116)
| ~ v1_relat_1(X117) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t97_relat_1])])]) ).
fof(c_0_66,plain,
! [X93,X94,X95] :
( k1_funct_4(X94,X95) = X95
| ~ m1_pboole(X95,X93)
| ~ m1_pboole(X94,X93)
| v1_xboole_0(X93) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])])]) ).
fof(c_0_67,plain,
! [X41] : m1_pboole(k1_pboole(X41),X41),
inference(variable_rename,[status(thm)],[dt_k1_pboole]) ).
cnf(c_0_68,negated_conjecture,
esk2_0 != k1_funct_4(k1_pboole(esk1_0),k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_69,plain,
k1_pboole(X1) = k2_funcop_1(X1,k1_xboole_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| k1_closure3(X1,X2) = a_2_0_closure3(X1,X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
( ~ r1_tarski(X2,X1)
| ~ r1_tarski(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_72,negated_conjecture,
r1_tarski(a_2_0_closure3(esk1_0,esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_49,c_0_58]) ).
cnf(c_0_73,negated_conjecture,
( ~ m1_pboole(esk2_0,X1)
| ~ r2_hidden(esk4_2(esk1_0,a_2_0_closure3(esk1_0,esk2_0)),X1)
| r1_tarski(esk1_0,a_2_0_closure3(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62])]) ).
cnf(c_0_74,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| m1_pboole(X1,k1_relat_1(X1)) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_75,negated_conjecture,
k1_relat_1(esk2_0) = esk1_0,
inference(spm,[status(thm)],[c_0_64,c_0_32]) ).
cnf(c_0_76,negated_conjecture,
v1_relat_1(esk2_0),
inference(spm,[status(thm)],[c_0_53,c_0_32]) ).
cnf(c_0_77,negated_conjecture,
v1_funct_1(esk2_0),
inference(spm,[status(thm)],[c_0_52,c_0_32]) ).
cnf(c_0_78,plain,
( ~ r1_tarski(k1_relat_1(X1),X2)
| ~ v1_relat_1(X1)
| k7_relat_1(X1,X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
fof(c_0_79,plain,
! [X92] : r1_tarski(X92,X92),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_80,plain,
( ~ m1_pboole(X3,X1)
| ~ m1_pboole(X2,X1)
| k1_funct_4(X2,X3) = X3
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_81,plain,
m1_pboole(k1_pboole(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_82,negated_conjecture,
esk2_0 != k1_funct_4(k2_funcop_1(esk1_0,k1_xboole_0),k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0))),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_83,negated_conjecture,
k1_closure3(esk1_0,esk2_0) = a_2_0_closure3(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_32]),c_0_33]) ).
cnf(c_0_84,negated_conjecture,
( ~ r1_tarski(esk1_0,a_2_0_closure3(esk1_0,esk2_0))
| a_2_0_closure3(esk1_0,esk2_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_85,negated_conjecture,
r1_tarski(esk1_0,a_2_0_closure3(esk1_0,esk2_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_76]),c_0_77])]),c_0_25]) ).
cnf(c_0_86,negated_conjecture,
( ~ r1_tarski(esk1_0,X1)
| k7_relat_1(esk2_0,X1) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_75]),c_0_76])]) ).
cnf(c_0_87,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_88,negated_conjecture,
( ~ m1_pboole(X1,esk1_0)
| k1_funct_4(X1,esk2_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_32]),c_0_33]) ).
cnf(c_0_89,plain,
m1_pboole(k2_funcop_1(X1,k1_xboole_0),X1),
inference(rw,[status(thm)],[c_0_81,c_0_69]) ).
cnf(c_0_90,negated_conjecture,
k1_funct_4(k2_funcop_1(esk1_0,k1_xboole_0),k7_relat_1(esk2_0,a_2_0_closure3(esk1_0,esk2_0))) != esk2_0,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,negated_conjecture,
a_2_0_closure3(esk1_0,esk2_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_92,negated_conjecture,
k7_relat_1(esk2_0,esk1_0) = esk2_0,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
k1_funct_4(k2_funcop_1(esk1_0,k1_xboole_0),esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG225+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 13:04:06 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 271.44/35.78 % Version: 3.5.1
% 271.44/35.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 271.44/35.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 271.44/35.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 271.44/35.78 % Starting new_bool_3 with 300s (1) cores
% 271.44/35.78 % Starting new_bool_1 with 300s (1) cores
% 271.44/35.78 % Starting sh5l with 300s (1) cores
% 271.44/35.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1148364 completed with status 0
% 271.44/35.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 271.44/35.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 271.44/35.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 271.44/35.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 271.44/35.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 271.44/35.78 % No SInE strategy applied
% 271.44/35.78 % Search class: FGHSM-FFMM31-MFFFFFNN
% 271.44/35.78 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 271.44/35.78 % Starting SubtermCWHack with 136s (1) cores
% 271.44/35.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 271.44/35.78 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 113s (1) cores
% 271.44/35.78 % Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SE_S0Y with 113s (1) cores
% 271.44/35.78 % Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 113s (1) cores
% 271.44/35.78 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1148371 completed with status 0
% 271.44/35.78 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 271.44/35.78 % Preprocessing class: FSLSSMSSSSSNFFN.
% 271.44/35.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 271.44/35.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 271.44/35.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 271.44/35.78 % No SInE strategy applied
% 271.44/35.78 % Search class: FGHSM-FFMM31-MFFFFFNN
% 271.44/35.78 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 271.44/35.78 % Starting SubtermCWHack with 136s (1) cores
% 271.44/35.78 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 271.44/35.78 % Preprocessing time : 0.004 s
% 271.44/35.78 % Presaturation interreduction done
% 271.44/35.78
% 271.44/35.78 % Proof found!
% 271.44/35.78 % SZS status Theorem
% 271.44/35.78 % SZS output start CNFRefutation
% See solution above
% 271.44/35.78 % Parsed axioms : 66
% 271.44/35.78 % Removed by relevancy pruning/SinE : 0
% 271.44/35.78 % Initial clauses : 124
% 271.44/35.78 % Removed in clause preprocessing : 10
% 271.44/35.78 % Initial clauses in saturation : 114
% 271.44/35.78 % Processed clauses : 79523
% 271.44/35.78 % ...of these trivial : 13
% 271.44/35.78 % ...subsumed : 69996
% 271.44/35.78 % ...remaining for further processing : 9514
% 271.44/35.78 % Other redundant clauses eliminated : 761
% 271.44/35.78 % Clauses deleted for lack of memory : 0
% 271.44/35.78 % Backward-subsumed : 874
% 271.44/35.78 % Backward-rewritten : 328
% 271.44/35.78 % Generated clauses : 951154
% 271.44/35.78 % ...of the previous two non-redundant : 914479
% 271.44/35.78 % ...aggressively subsumed : 0
% 271.44/35.78 % Contextual simplify-reflections : 301
% 271.44/35.78 % Paramodulations : 950311
% 271.44/35.78 % Factorizations : 82
% 271.44/35.78 % NegExts : 0
% 271.44/35.78 % Equation resolutions : 761
% 271.44/35.78 % Disequality decompositions : 0
% 271.44/35.78 % Total rewrite steps : 165223
% 271.44/35.78 % ...of those cached : 164044
% 271.44/35.78 % Propositional unsat checks : 1
% 271.44/35.78 % Propositional check models : 0
% 271.44/35.78 % Propositional check unsatisfiable : 0
% 271.44/35.78 % Propositional clauses : 0
% 271.44/35.78 % Propositional clauses after purity: 0
% 271.44/35.78 % Propositional unsat core size : 0
% 271.44/35.78 % Propositional preprocessing time : 0.000
% 271.44/35.78 % Propositional encoding time : 0.627
% 271.44/35.78 % Propositional solver time : 0.282
% 271.44/35.78 % Success case prop preproc time : 0.000
% 271.44/35.78 % Success case prop encoding time : 0.000
% 271.44/35.78 % Success case prop solver time : 0.000
% 271.44/35.78 % Current number of processed clauses : 8199
% 271.44/35.78 % Positive orientable unit clauses : 138
% 271.44/35.78 % Positive unorientable unit clauses: 0
% 271.44/35.78 % Negative unit clauses : 22
% 271.44/35.78 % Non-unit-clauses : 8039
% 271.44/35.78 % Current number of unprocessed clauses: 826267
% 271.44/35.78 % ...number of literals in the above : 5098798
% 271.44/35.78 % Current number of archived formulas : 0
% 271.44/35.78 % Current number of archived clauses : 1309
% 271.44/35.78 % Clause-clause subsumption calls (NU) : 19923119
% 271.44/35.78 % Rec. Clause-clause subsumption calls : 4269566
% 271.44/35.78 % Non-unit clause-clause subsumptions : 52509
% 271.44/35.78 % Unit Clause-clause subsumption calls : 53140
% 271.44/35.78 % Rewrite failures with RHS unbound : 0
% 271.44/35.78 % BW rewrite match attempts : 152
% 271.44/35.78 % BW rewrite match successes : 19
% 271.44/35.78 % Condensation attempts : 0
% 271.44/35.78 % Condensation successes : 0
% 271.44/35.78 % Termbank termtop insertions : 21776936
% 271.44/35.78 % Search garbage collected termcells : 1217
% 271.44/35.78
% 271.44/35.78 % -------------------------------------------------
% 271.44/35.78 % User time : 33.943 s
% 271.44/35.78 % System time : 0.835 s
% 271.44/35.78 % Total time : 34.778 s
% 271.44/35.78 % Maximum resident set size: 3944 pages
% 271.44/35.78
% 271.44/35.78 % -------------------------------------------------
% 271.44/35.78 % User time : 169.514 s
% 271.44/35.78 % System time : 5.136 s
% 271.44/35.78 % Total time : 174.650 s
% 271.44/35.78 % Maximum resident set size: 4864 pages
% 271.44/35.78 % E exiting
%------------------------------------------------------------------------------