%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG226+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 : n014.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 11:55:40 AM UTC 2026
% Result : Theorem 23.95s 4.08s
% Output : CNFRefutation 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 88 ( 25 unt; 0 def)
% Number of atoms : 326 ( 106 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 374 ( 136 ~; 150 |; 49 &)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 147 ( 2 sgn 86 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_closure3,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_closure3) ).
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(t9_funct_1,axiom,
! [X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( ( ! [X3] :
( r2_hidden(X3,k1_relat_1(X1))
=> k1_funct_1(X1,X3) = k1_funct_1(X2,X3) )
& k1_relat_1(X1) = k1_relat_1(X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
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(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(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k3_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t90_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> k1_relat_1(k7_relat_1(X2,X1)) = k3_xboole_0(k1_relat_1(X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(fc2_pboole,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,X1)
& m1_pboole(X2,X1)
& v2_relat_1(X2)
& ~ v1_xboole_0(X1) )
=> ~ v1_xboole_0(k1_funct_1(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
fof(t70_funct_1,axiom,
! [X1,X2,X3] :
( ( v1_funct_1(X3)
& v1_relat_1(X3) )
=> ( r2_hidden(X2,k1_relat_1(k7_relat_1(X3,X1)))
=> k1_funct_1(k7_relat_1(X3,X1),X2) = k1_funct_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(redefinition_r6_pboole,axiom,
! [X1,X2,X3] :
( ( m1_pboole(X3,X1)
& m1_pboole(X2,X1) )
=> ( r6_pboole(X1,X2,X3)
<=> X2 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r6_pboole) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t7_closure3]) ).
fof(c_0_15,plain,
! [X29,X30] :
( ( ~ v1_funct_1(X30)
| ~ v1_relat_1(X30)
| m1_pboole(X30,X29)
| k1_relat_1(X30) != X29 )
& ( ~ v1_funct_1(X30)
| ~ v1_relat_1(X30)
| k1_relat_1(X30) = X29
| ~ m1_pboole(X30,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pboole])])])]) ).
fof(c_0_16,plain,
! [X42,X43] :
( ( ~ m1_pboole(X43,X42)
| v1_funct_1(X43) )
& ( ~ m1_pboole(X43,X42)
| v1_relat_1(X43) ) ),
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_17,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( ( m1_pboole(X2,X1)
& v2_relat_1(X2) )
=> ! [X3] :
( ( m1_pboole(X3,X1)
& v2_relat_1(X3) )
=> ( ( k7_relat_1(X2,k1_closure3(X1,X2)) = k7_relat_1(X3,k1_closure3(X1,X3))
& k1_closure3(X1,X2) = k1_closure3(X1,X3) )
=> r6_pboole(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
cnf(c_0_18,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_15]) ).
cnf(c_0_19,plain,
( ~ m1_pboole(X1,X2)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ m1_pboole(X1,X2)
| v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,negated_conjecture,
( ~ r6_pboole(esk1_0,esk2_0,esk3_0)
& k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0))
& k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0)
& m1_pboole(esk3_0,esk1_0)
& v2_relat_1(esk3_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_17])])])]) ).
fof(c_0_22,plain,
! [X109,X110] :
( ( ~ v1_funct_1(X109)
| ~ v1_relat_1(X109)
| ~ v1_funct_1(X110)
| ~ v1_relat_1(X110)
| X109 = X110
| k1_relat_1(X109) != k1_relat_1(X110)
| k1_funct_1(X109,esk23_2(X109,X110)) != k1_funct_1(X110,esk23_2(X109,X110)) )
& ( ~ v1_funct_1(X109)
| ~ v1_relat_1(X109)
| ~ v1_funct_1(X110)
| ~ v1_relat_1(X110)
| X109 = X110
| k1_relat_1(X109) != k1_relat_1(X110)
| r2_hidden(esk23_2(X109,X110),k1_relat_1(X109)) ) ),
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)],[t9_funct_1])])])])])]) ).
cnf(c_0_23,plain,
( ~ m1_pboole(X1,X2)
| k1_relat_1(X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
m1_pboole(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,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]) ).
cnf(c_0_26,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| k1_relat_1(X1) != k1_relat_1(X2)
| X1 = X2
| r2_hidden(esk23_2(X1,X2),k1_relat_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
k1_relat_1(esk3_0) = esk1_0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
v1_relat_1(esk3_0),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
v1_funct_1(esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
m1_pboole(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,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_32,plain,
! [X57,X58,X59,X61] :
( ( ~ m1_pboole(X59,X58)
| v1_xboole_0(X58)
| r2_hidden(X57,a_2_0_closure3(X58,X59))
| k1_funct_1(X59,X61) = k1_xboole_0
| X57 != X61
| ~ m1_subset_1(X61,X58) )
& ( ~ m1_pboole(X59,X58)
| v1_xboole_0(X58)
| ~ r2_hidden(X57,a_2_0_closure3(X58,X59))
| k1_funct_1(X59,esk8_3(X57,X58,X59)) != k1_xboole_0 )
& ( ~ m1_pboole(X59,X58)
| v1_xboole_0(X58)
| ~ r2_hidden(X57,a_2_0_closure3(X58,X59))
| X57 = esk8_3(X57,X58,X59) )
& ( ~ m1_pboole(X59,X58)
| v1_xboole_0(X58)
| ~ r2_hidden(X57,a_2_0_closure3(X58,X59))
| m1_subset_1(esk8_3(X57,X58,X59),X58) ) ),
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_25])])])])])]) ).
fof(c_0_33,plain,
! [X91,X92] :
( m1_subset_1(X91,X92)
| ~ r2_hidden(X91,X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_relat_1(X1) != esk1_0
| r2_hidden(esk23_2(X1,esk3_0),k1_relat_1(X1))
| X1 = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_35,negated_conjecture,
k1_relat_1(esk2_0) = esk1_0,
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
v1_relat_1(esk2_0),
inference(spm,[status(thm)],[c_0_20,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
v1_funct_1(esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
fof(c_0_38,plain,
! [X26,X27,X28] :
( ( v1_xboole_0(X26)
| ~ m1_pboole(X27,X26)
| X28 = k1_closure3(X26,X27)
| X28 != a_2_0_closure3(X26,X27) )
& ( v1_xboole_0(X26)
| ~ m1_pboole(X27,X26)
| X28 = a_2_0_closure3(X26,X27)
| X28 != k1_closure3(X26,X27) ) ),
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_31])])])])]) ).
fof(c_0_39,plain,
! [X31,X32,X33,X34,X35,X36,X37,X38] :
( ( X38 = k3_xboole_0(X36,X37)
| r2_hidden(esk5_3(X36,X37,X38),X38)
| r2_hidden(esk5_3(X36,X37,X38),X37) )
& ( X38 = k3_xboole_0(X36,X37)
| r2_hidden(esk5_3(X36,X37,X38),X38)
| r2_hidden(esk5_3(X36,X37,X38),X36) )
& ( X38 = k3_xboole_0(X36,X37)
| ~ r2_hidden(esk5_3(X36,X37,X38),X37)
| ~ r2_hidden(esk5_3(X36,X37,X38),X36)
| ~ r2_hidden(esk5_3(X36,X37,X38),X38) )
& ( X33 != k3_xboole_0(X31,X32)
| r2_hidden(X35,X33)
| ~ r2_hidden(X35,X32)
| ~ r2_hidden(X35,X31) )
& ( X33 != k3_xboole_0(X31,X32)
| ~ r2_hidden(X34,X33)
| r2_hidden(X34,X32) )
& ( X33 != k3_xboole_0(X31,X32)
| ~ r2_hidden(X34,X33)
| r2_hidden(X34,X31) ) ),
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_xboole_0])])])])])])]) ).
cnf(c_0_40,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_32]) ).
cnf(c_0_41,plain,
( ~ r2_hidden(X1,X2)
| m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( r2_hidden(esk23_2(esk2_0,esk3_0),esk1_0)
| esk3_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_43,plain,
( ~ m1_pboole(X3,X2)
| X1 != a_2_0_closure3(X2,X3)
| v1_xboole_0(X2)
| X1 = k1_closure3(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_44,plain,
! [X107,X108] :
( k1_relat_1(k7_relat_1(X108,X107)) = k3_xboole_0(k1_relat_1(X108),X107)
| ~ v1_relat_1(X108) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_relat_1])])]) ).
cnf(c_0_45,plain,
( X4 != k3_xboole_0(X2,X3)
| ~ r2_hidden(X1,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,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_40]) ).
cnf(c_0_47,negated_conjecture,
( m1_subset_1(esk23_2(esk2_0,esk3_0),esk1_0)
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_49,plain,
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| a_2_0_closure3(X1,X2) = k1_closure3(X1,X2) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
k1_closure3(esk1_0,esk2_0) = k1_closure3(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_51,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,X1)
& m1_pboole(X2,X1)
& v2_relat_1(X2)
& ~ v1_xboole_0(X1) )
=> ~ v1_xboole_0(k1_funct_1(X2,X3)) ),
inference(fof_simplification,[status(thm)],[fc2_pboole]) ).
fof(c_0_52,plain,
! [X100,X101,X102] :
( k1_funct_1(k7_relat_1(X102,X100),X101) = k1_funct_1(X102,X101)
| ~ r2_hidden(X101,k1_relat_1(k7_relat_1(X102,X100)))
| ~ v1_funct_1(X102)
| ~ v1_relat_1(X102) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t70_funct_1])])]) ).
cnf(c_0_53,plain,
( ~ v1_relat_1(X1)
| k1_relat_1(k7_relat_1(X1,X2)) = k3_xboole_0(k1_relat_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( ~ r2_hidden(X1,X2)
| ~ r2_hidden(X1,X3)
| r2_hidden(X1,k3_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( ~ m1_pboole(X1,esk1_0)
| r2_hidden(esk23_2(esk2_0,esk3_0),a_2_0_closure3(esk1_0,X1))
| esk3_0 = esk2_0
| k1_funct_1(X1,esk23_2(esk2_0,esk3_0)) = k1_xboole_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_56,negated_conjecture,
a_2_0_closure3(esk1_0,esk3_0) = k1_closure3(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_24]),c_0_50]),c_0_48]) ).
fof(c_0_57,plain,
! [X20,X21] : k3_xboole_0(X20,X21) = k3_xboole_0(X21,X20),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_58,plain,
! [X52,X53,X54] :
( ~ v1_xboole_0(k1_funct_1(X53,X54))
| ~ m1_subset_1(X54,X52)
| ~ m1_pboole(X53,X52)
| ~ v2_relat_1(X53)
| v1_xboole_0(X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
cnf(c_0_59,plain,
( ~ r2_hidden(X2,k1_relat_1(k7_relat_1(X1,X3)))
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_funct_1(k7_relat_1(X1,X3),X2) = k1_funct_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,negated_conjecture,
k1_relat_1(k7_relat_1(esk3_0,X1)) = k3_xboole_0(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_28]),c_0_27]) ).
cnf(c_0_61,negated_conjecture,
( ~ r2_hidden(esk23_2(esk2_0,esk3_0),X1)
| r2_hidden(esk23_2(esk2_0,esk3_0),k3_xboole_0(X1,esk1_0))
| esk3_0 = esk2_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_62,negated_conjecture,
( r2_hidden(esk23_2(esk2_0,esk3_0),k1_closure3(esk1_0,esk2_0))
| esk3_0 = esk2_0
| k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) = k1_xboole_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_24]),c_0_56]) ).
cnf(c_0_63,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,negated_conjecture,
k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk3_0,k1_closure3(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_65,negated_conjecture,
k1_relat_1(k7_relat_1(esk2_0,X1)) = k3_xboole_0(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_35]) ).
cnf(c_0_66,plain,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| k1_relat_1(X1) != k1_relat_1(X2)
| k1_funct_1(X1,esk23_2(X1,X2)) != k1_funct_1(X2,esk23_2(X1,X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_67,plain,
( ~ v1_xboole_0(k1_funct_1(X2,X3))
| ~ m1_subset_1(X3,X1)
| ~ m1_pboole(X2,X1)
| ~ v2_relat_1(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,negated_conjecture,
( ~ r2_hidden(X2,k3_xboole_0(esk1_0,X1))
| k1_funct_1(k7_relat_1(esk3_0,X1),X2) = k1_funct_1(esk3_0,X2) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_29]),c_0_28])]),c_0_60]) ).
cnf(c_0_69,negated_conjecture,
( r2_hidden(esk23_2(esk2_0,esk3_0),k3_xboole_0(esk1_0,k1_closure3(esk1_0,esk2_0)))
| esk3_0 = esk2_0
| k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) = k1_xboole_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_70,negated_conjecture,
k7_relat_1(esk3_0,k1_closure3(esk1_0,esk2_0)) = k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)),
inference(rw,[status(thm)],[c_0_64,c_0_50]) ).
cnf(c_0_71,negated_conjecture,
( ~ r2_hidden(X2,k3_xboole_0(esk1_0,X1))
| k1_funct_1(k7_relat_1(esk2_0,X1),X2) = k1_funct_1(esk2_0,X2) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_37]),c_0_36])]),c_0_65]) ).
cnf(c_0_72,negated_conjecture,
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_relat_1(X1) != esk1_0
| k1_funct_1(X1,esk23_2(X1,esk3_0)) != k1_funct_1(esk3_0,esk23_2(X1,esk3_0))
| X1 = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_27]),c_0_28]),c_0_29])]) ).
fof(c_0_73,plain,
! [X82,X83,X84] :
( ( ~ m1_pboole(X84,X82)
| ~ m1_pboole(X83,X82)
| r6_pboole(X82,X83,X84)
| X83 != X84 )
& ( ~ m1_pboole(X84,X82)
| ~ m1_pboole(X83,X82)
| X83 = X84
| ~ r6_pboole(X82,X83,X84) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r6_pboole])])])]) ).
cnf(c_0_74,negated_conjecture,
( ~ v1_xboole_0(k1_funct_1(X1,esk23_2(esk2_0,esk3_0)))
| ~ v2_relat_1(X1)
| ~ m1_pboole(X1,esk1_0)
| esk3_0 = esk2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_47]),c_0_48]) ).
cnf(c_0_75,negated_conjecture,
v2_relat_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_76,negated_conjecture,
( esk3_0 = esk2_0
| k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) = k1_xboole_0
| k1_funct_1(k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)),esk23_2(esk2_0,esk3_0)) = k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( esk3_0 = esk2_0
| k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) = k1_xboole_0
| k1_funct_1(k7_relat_1(esk2_0,k1_closure3(esk1_0,esk2_0)),esk23_2(esk2_0,esk3_0)) = k1_funct_1(esk2_0,esk23_2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) != k1_funct_1(esk2_0,esk23_2(esk2_0,esk3_0))
| esk3_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_79,plain,
( ~ m1_pboole(X2,X3)
| ~ m1_pboole(X1,X3)
| X1 != X2
| r6_pboole(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( ~ v1_xboole_0(k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)))
| esk3_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_24])]) ).
cnf(c_0_81,negated_conjecture,
( esk3_0 = esk2_0
| k1_funct_1(esk3_0,esk23_2(esk2_0,esk3_0)) = k1_xboole_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_82,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_83,plain,
( ~ m1_pboole(X2,X1)
| r6_pboole(X1,X2,X2) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_84,negated_conjecture,
~ r6_pboole(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_85,negated_conjecture,
esk3_0 = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_86,negated_conjecture,
r6_pboole(esk1_0,esk2_0,esk2_0),
inference(spm,[status(thm)],[c_0_83,c_0_30]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85]),c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG226+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 13:06:34 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.51 Running first-order theorem proving
% 0.19/0.51 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
% 23.95/4.08 % Version: 3.5.1
% 23.95/4.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 23.95/4.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.95/4.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 23.95/4.08 % Starting new_bool_3 with 300s (1) cores
% 23.95/4.08 % Starting new_bool_1 with 300s (1) cores
% 23.95/4.08 % Starting sh5l with 300s (1) cores
% 23.95/4.08 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 4131336 completed with status 0
% 23.95/4.08 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 23.95/4.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 23.95/4.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.95/4.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 23.95/4.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.95/4.08 % No SInE strategy applied
% 23.95/4.08 % Search class: FGHSM-FFMM31-SFFFFFNN
% 23.95/4.08 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 23.95/4.08 % Starting SubtermCWHack with 136s (1) cores
% 23.95/4.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 23.95/4.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 23.95/4.08 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 23.95/4.08 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 23.95/4.08 % G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 4131342 completed with status 0
% 23.95/4.08 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 23.95/4.08 % Preprocessing class: FSLSSMSSSSSNFFN.
% 23.95/4.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.95/4.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 23.95/4.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.95/4.08 % No SInE strategy applied
% 23.95/4.08 % Search class: FGHSM-FFMM31-SFFFFFNN
% 23.95/4.08 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 23.95/4.08 % Starting SubtermCWHack with 136s (1) cores
% 23.95/4.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 23.95/4.08 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 23.95/4.08 % Preprocessing time : 0.004 s
% 23.95/4.08 % Presaturation interreduction done
% 23.95/4.08
% 23.95/4.08 % Proof found!
% 23.95/4.08 % SZS status Theorem
% 23.95/4.08 % SZS output start CNFRefutation
% See solution above
% 23.95/4.08 % Parsed axioms : 57
% 23.95/4.08 % Removed by relevancy pruning/SinE : 0
% 23.95/4.08 % Initial clauses : 109
% 23.95/4.08 % Removed in clause preprocessing : 8
% 23.95/4.08 % Initial clauses in saturation : 101
% 23.95/4.08 % Processed clauses : 10752
% 23.95/4.08 % ...of these trivial : 223
% 23.95/4.08 % ...subsumed : 6055
% 23.95/4.08 % ...remaining for further processing : 4474
% 23.95/4.08 % Other redundant clauses eliminated : 232
% 23.95/4.08 % Clauses deleted for lack of memory : 0
% 23.95/4.08 % Backward-subsumed : 135
% 23.95/4.08 % Backward-rewritten : 1648
% 23.95/4.08 % Generated clauses : 63852
% 23.95/4.08 % ...of the previous two non-redundant : 58796
% 23.95/4.08 % ...aggressively subsumed : 0
% 23.95/4.08 % Contextual simplify-reflections : 56
% 23.95/4.08 % Paramodulations : 63557
% 23.95/4.08 % Factorizations : 47
% 23.95/4.08 % NegExts : 0
% 23.95/4.08 % Equation resolutions : 248
% 23.95/4.08 % Disequality decompositions : 0
% 23.95/4.08 % Total rewrite steps : 47303
% 23.95/4.08 % ...of those cached : 46008
% 23.95/4.08 % Propositional unsat checks : 0
% 23.95/4.08 % Propositional check models : 0
% 23.95/4.08 % Propositional check unsatisfiable : 0
% 23.95/4.08 % Propositional clauses : 0
% 23.95/4.08 % Propositional clauses after purity: 0
% 23.95/4.08 % Propositional unsat core size : 0
% 23.95/4.08 % Propositional preprocessing time : 0.000
% 23.95/4.08 % Propositional encoding time : 0.000
% 23.95/4.08 % Propositional solver time : 0.000
% 23.95/4.08 % Success case prop preproc time : 0.000
% 23.95/4.08 % Success case prop encoding time : 0.000
% 23.95/4.08 % Success case prop solver time : 0.000
% 23.95/4.08 % Current number of processed clauses : 2585
% 23.95/4.08 % Positive orientable unit clauses : 376
% 23.95/4.08 % Positive unorientable unit clauses: 1
% 23.95/4.08 % Negative unit clauses : 7
% 23.95/4.08 % Non-unit-clauses : 2201
% 23.95/4.08 % Current number of unprocessed clauses: 46233
% 23.95/4.08 % ...number of literals in the above : 147683
% 23.95/4.08 % Current number of archived formulas : 0
% 23.95/4.08 % Current number of archived clauses : 1880
% 23.95/4.08 % Clause-clause subsumption calls (NU) : 623556
% 23.95/4.08 % Rec. Clause-clause subsumption calls : 459317
% 23.95/4.08 % Non-unit clause-clause subsumptions : 6024
% 23.95/4.08 % Unit Clause-clause subsumption calls : 15546
% 23.95/4.08 % Rewrite failures with RHS unbound : 0
% 23.95/4.08 % BW rewrite match attempts : 2374
% 23.95/4.08 % BW rewrite match successes : 83
% 23.95/4.08 % Condensation attempts : 0
% 23.95/4.08 % Condensation successes : 0
% 23.95/4.08 % Termbank termtop insertions : 1593358
% 23.95/4.08 % Search garbage collected termcells : 1287
% 23.95/4.08
% 23.95/4.08 % -------------------------------------------------
% 23.95/4.08 % User time : 3.000 s
% 23.95/4.08 % System time : 0.099 s
% 23.95/4.08 % Total time : 3.098 s
% 23.95/4.08 % Maximum resident set size: 3940 pages
% 23.95/4.08
% 23.95/4.08 % -------------------------------------------------
% 23.95/4.08 % User time : 16.332 s
% 23.95/4.08 % System time : 0.519 s
% 23.95/4.08 % Total time : 16.851 s
% 23.95/4.08 % Maximum resident set size: 4608 pages
% 23.95/4.08 % E exiting
%------------------------------------------------------------------------------