%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP624+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 : n001.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 12:40:25 PM UTC 2026
% Result : Theorem 3.55s 1.32s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 14 unt; 0 def)
% Number of atoms : 361 ( 26 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 462 ( 169 ~; 169 |; 85 &)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 121 ( 2 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t15_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_autgroup) ).
fof(t13_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(dt_k2_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_1(k2_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_autgroup) ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(d2_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_1(X2) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_autgroup) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(assume_negation,[status(cth)],[t15_autgroup]) ).
fof(c_0_12,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[t13_autgroup]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_1(k2_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_autgroup]) ).
fof(c_0_15,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( v1_fraenkel(X3)
& ~ v1_xboole_0(X3) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).
fof(c_0_16,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_autgroup]) ).
fof(c_0_17,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
fof(c_0_18,plain,
! [X137,X138] :
( m2_fraenkel(X138,u1_struct_0(X137),u1_struct_0(X137),k1_autgroup(X137))
| ~ m2_fraenkel(X138,u1_struct_0(X137),u1_struct_0(X137),k4_autgroup(X137))
| ~ l1_group_1(X137)
| ~ v4_group_1(X137)
| ~ v3_group_1(X137)
| ~ v1_group_1(X137)
| v3_struct_0(X137) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_19,negated_conjecture,
( k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0)
& m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_20,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& v1_funct_1(X2) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d2_autgroup]) ).
fof(c_0_21,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,X2)
& m1_subset_1(X5,X1)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2)
& ~ v1_xboole_0(X1) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1]) ).
fof(c_0_22,plain,
! [X133,X134,X135] :
( ( m2_relset_1(X135,X133,X134)
| ~ m1_relset_1(X135,X133,X134) )
& ( m1_relset_1(X135,X133,X134)
| ~ m2_relset_1(X135,X133,X134) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_23,plain,
! [X46] :
( ( ~ l1_group_1(X46)
| ~ v4_group_1(X46)
| ~ v3_group_1(X46)
| ~ v1_group_1(X46)
| v3_struct_0(X46)
| m2_relset_1(k2_autgroup(X46),k2_zfmisc_1(k1_autgroup(X46),k1_autgroup(X46)),k1_autgroup(X46)) )
& ( ~ l1_group_1(X46)
| ~ v4_group_1(X46)
| ~ v3_group_1(X46)
| ~ v1_group_1(X46)
| v3_struct_0(X46)
| v1_funct_2(k2_autgroup(X46),k2_zfmisc_1(k1_autgroup(X46),k1_autgroup(X46)),k1_autgroup(X46)) )
& ( ~ l1_group_1(X46)
| ~ v4_group_1(X46)
| ~ v3_group_1(X46)
| ~ v1_group_1(X46)
| v3_struct_0(X46)
| v1_funct_1(k2_autgroup(X46)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_24,plain,
! [X62,X63,X64] :
( ( ~ m1_fraenkel(X64,X62,X63)
| v1_fraenkel(X64) )
& ( ~ m1_fraenkel(X64,X62,X63)
| ~ v1_xboole_0(X64) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_25,plain,
! [X45] :
( m1_fraenkel(k1_autgroup(X45),u1_struct_0(X45),u1_struct_0(X45))
| ~ l1_group_1(X45)
| ~ v4_group_1(X45)
| ~ v3_group_1(X45)
| ~ v1_group_1(X45)
| v3_struct_0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_26,plain,
! [X129,X130,X131,X132] :
( ( ~ m1_fraenkel(X131,X129,X130)
| v1_xboole_0(X130)
| m2_fraenkel(X132,X129,X130,X131)
| ~ m1_subset_1(X132,X131) )
& ( ~ m1_fraenkel(X131,X129,X130)
| v1_xboole_0(X130)
| m1_subset_1(X132,X131)
| ~ m2_fraenkel(X132,X129,X130,X131) ) ),
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_17])])])])]) ).
cnf(c_0_27,plain,
( ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_34,plain,
! [X35,X36,X37,X38] :
( ( ~ l1_group_1(X35)
| ~ v4_group_1(X35)
| ~ v3_group_1(X35)
| ~ v1_group_1(X35)
| v3_struct_0(X35)
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_1(X36)
| X36 = k2_autgroup(X35)
| k2_binop_1(k1_autgroup(X35),k1_autgroup(X35),k1_autgroup(X35),X36,esk4_2(X35,X36),esk5_2(X35,X36)) != k7_funct_2(u1_struct_0(X35),u1_struct_0(X35),u1_struct_0(X35),esk5_2(X35,X36),esk4_2(X35,X36)) )
& ( ~ l1_group_1(X35)
| ~ v4_group_1(X35)
| ~ v3_group_1(X35)
| ~ v1_group_1(X35)
| v3_struct_0(X35)
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_1(X36)
| X36 = k2_autgroup(X35)
| m2_fraenkel(esk5_2(X35,X36),u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35)) )
& ( ~ l1_group_1(X35)
| ~ v4_group_1(X35)
| ~ v3_group_1(X35)
| ~ v1_group_1(X35)
| v3_struct_0(X35)
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_1(X36)
| X36 = k2_autgroup(X35)
| m2_fraenkel(esk4_2(X35,X36),u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35)) )
& ( ~ l1_group_1(X35)
| ~ v4_group_1(X35)
| ~ v3_group_1(X35)
| ~ v1_group_1(X35)
| v3_struct_0(X35)
| ~ m2_relset_1(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_2(X36,k2_zfmisc_1(k1_autgroup(X35),k1_autgroup(X35)),k1_autgroup(X35))
| ~ v1_funct_1(X36)
| k2_binop_1(k1_autgroup(X35),k1_autgroup(X35),k1_autgroup(X35),X36,X37,X38) = k7_funct_2(u1_struct_0(X35),u1_struct_0(X35),u1_struct_0(X35),X38,X37)
| ~ m2_fraenkel(X38,u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| ~ m2_fraenkel(X37,u1_struct_0(X35),u1_struct_0(X35),k1_autgroup(X35))
| X36 != k2_autgroup(X35) ) ),
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_20])])])])])]) ).
fof(c_0_35,plain,
! [X118,X119,X120,X121,X122,X123] :
( k2_binop_1(X118,X119,X120,X121,X122,X123) = k1_binop_1(X121,X122,X123)
| ~ m1_subset_1(X123,X119)
| ~ m1_subset_1(X122,X118)
| ~ m1_relset_1(X121,k2_zfmisc_1(X118,X119),X120)
| ~ v1_funct_2(X121,k2_zfmisc_1(X118,X119),X120)
| ~ v1_funct_1(X121)
| v1_xboole_0(X119)
| v1_xboole_0(X118) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_36,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_37,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_38,plain,
( ~ m1_fraenkel(X1,X2,X3)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| m1_subset_1(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,plain,
( ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2)
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| ~ v1_funct_1(X1)
| ~ m2_fraenkel(X4,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ m2_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| X1 != k2_autgroup(X2)
| v3_struct_0(X2)
| k2_binop_1(k1_autgroup(X2),k1_autgroup(X2),k1_autgroup(X2),X1,X3,X4) = k7_funct_2(u1_struct_0(X2),u1_struct_0(X2),u1_struct_0(X2),X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| v1_funct_1(k2_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_45,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| v3_struct_0(X1)
| v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_46,plain,
( ~ m1_subset_1(X6,X2)
| ~ m1_subset_1(X5,X1)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X4)
| ~ v1_funct_1(X3)
| k2_binop_1(X1,X2,X4,X3,X5,X6) = k1_binop_1(X3,X5,X6)
| v1_xboole_0(X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| v3_struct_0(X1)
| m1_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_48,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_xboole_0(k1_autgroup(X1))
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_51,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| v3_struct_0(X1)
| k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_44]),c_0_45]),c_0_37]) ).
fof(c_0_52,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
cnf(c_0_53,plain,
( ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| v3_struct_0(X1)
| k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),k2_autgroup(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_44]),c_0_47]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_39]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_55,negated_conjecture,
( ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| m1_subset_1(esk2_0,k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( ~ m2_fraenkel(X1,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(esk1_0))
| k2_binop_1(k1_autgroup(esk1_0),k1_autgroup(esk1_0),k1_autgroup(esk1_0),k2_autgroup(esk1_0),X1,esk3_0) = k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_41]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
fof(c_0_57,plain,
! [X94] :
( ~ v1_xboole_0(u1_struct_0(X94))
| ~ l1_struct_0(X94)
| v3_struct_0(X94) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_58,negated_conjecture,
( ~ m1_subset_1(X1,k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0))
| k2_binop_1(k1_autgroup(esk1_0),k1_autgroup(esk1_0),k1_autgroup(esk1_0),k2_autgroup(esk1_0),X1,esk3_0) = k1_binop_1(k2_autgroup(esk1_0),X1,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_59,negated_conjecture,
( m1_subset_1(esk2_0,k1_autgroup(esk1_0))
| v1_xboole_0(u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_39]),c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_60,negated_conjecture,
k2_binop_1(k1_autgroup(esk1_0),k1_autgroup(esk1_0),k1_autgroup(esk1_0),k2_autgroup(esk1_0),esk2_0,esk3_0) = k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_56,c_0_50]) ).
cnf(c_0_61,negated_conjecture,
k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_62,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,negated_conjecture,
v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61]) ).
fof(c_0_64,plain,
! [X61] :
( l1_struct_0(X61)
| ~ l1_group_1(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])])]) ).
cnf(c_0_65,negated_conjecture,
~ l1_struct_0(esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_33]) ).
cnf(c_0_66,plain,
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP624+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.65 % Computer : n001.cluster.edu
% 0.19/0.65 % Model : x86_64 x86_64
% 0.19/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.65 % Memory : 8046.5625MB
% 0.19/0.65 % OS : Linux 6.8.0-71-generic
% 0.19/0.65 % CPULimit : 300
% 0.19/0.65 % WCLimit : 300
% 0.19/0.65 % DateTime : Sun Sep 20 20:25:13 UTC 2026
% 0.22/0.65 % CPUTime :
% 0.22/0.65 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.72 Running first-order theorem proving
% 0.22/0.72 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
% 3.55/1.32 % Version: 3.5.1
% 3.55/1.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.55/1.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.55/1.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.55/1.32 % Starting new_bool_3 with 300s (1) cores
% 3.55/1.32 % Starting new_bool_1 with 300s (1) cores
% 3.55/1.32 % Starting sh5l with 300s (1) cores
% 3.55/1.32 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1329898 completed with status 0
% 3.55/1.32 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.55/1.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.55/1.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.55/1.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.55/1.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.55/1.32 % No SInE strategy applied
% 3.55/1.32 % Search class: FGHSM-FFMM32-MFFFFFNN
% 3.55/1.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.55/1.32 % Starting SubtermCWHack with 136s (1) cores
% 3.55/1.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.55/1.32 % Starting G-E--_300_C18_F1_URBAN_S0Y with 369s (1) cores
% 3.55/1.32 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 3.55/1.32 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 3.55/1.32 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1329906 completed with status 0
% 3.55/1.32 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.55/1.32 % Preprocessing class: FSLSSMSSSSSNFFN.
% 3.55/1.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.55/1.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 3.55/1.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.55/1.32 % No SInE strategy applied
% 3.55/1.32 % Search class: FGHSM-FFMM32-MFFFFFNN
% 3.55/1.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.55/1.32 % Starting SubtermCWHack with 136s (1) cores
% 3.55/1.32 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 3.55/1.32 % Preprocessing time : 0.004 s
% 3.55/1.32 % Presaturation interreduction done
% 3.55/1.32
% 3.55/1.32 % Proof found!
% 3.55/1.32 % SZS status Theorem
% 3.55/1.32 % SZS output start CNFRefutation
% See solution above
% 3.55/1.32 % Parsed axioms : 79
% 3.55/1.32 % Removed by relevancy pruning/SinE : 0
% 3.55/1.32 % Initial clauses : 139
% 3.55/1.32 % Removed in clause preprocessing : 21
% 3.55/1.32 % Initial clauses in saturation : 118
% 3.55/1.32 % Processed clauses : 2535
% 3.55/1.32 % ...of these trivial : 4
% 3.55/1.32 % ...subsumed : 1551
% 3.55/1.32 % ...remaining for further processing : 980
% 3.55/1.32 % Other redundant clauses eliminated : 15
% 3.55/1.32 % Clauses deleted for lack of memory : 0
% 3.55/1.32 % Backward-subsumed : 22
% 3.55/1.32 % Backward-rewritten : 133
% 3.55/1.32 % Generated clauses : 7852
% 3.55/1.32 % ...of the previous two non-redundant : 7172
% 3.55/1.32 % ...aggressively subsumed : 0
% 3.55/1.32 % Contextual simplify-reflections : 71
% 3.55/1.32 % Paramodulations : 7835
% 3.55/1.32 % Factorizations : 0
% 3.55/1.32 % NegExts : 0
% 3.55/1.32 % Equation resolutions : 17
% 3.55/1.32 % Disequality decompositions : 0
% 3.55/1.32 % Total rewrite steps : 1222
% 3.55/1.32 % ...of those cached : 1136
% 3.55/1.32 % Propositional unsat checks : 0
% 3.55/1.32 % Propositional check models : 0
% 3.55/1.32 % Propositional check unsatisfiable : 0
% 3.55/1.32 % Propositional clauses : 0
% 3.55/1.32 % Propositional clauses after purity: 0
% 3.55/1.32 % Propositional unsat core size : 0
% 3.55/1.32 % Propositional preprocessing time : 0.000
% 3.55/1.32 % Propositional encoding time : 0.000
% 3.55/1.32 % Propositional solver time : 0.000
% 3.55/1.32 % Success case prop preproc time : 0.000
% 3.55/1.32 % Success case prop encoding time : 0.000
% 3.55/1.32 % Success case prop solver time : 0.000
% 3.55/1.32 % Current number of processed clauses : 709
% 3.55/1.32 % Positive orientable unit clauses : 74
% 3.55/1.32 % Positive unorientable unit clauses: 1
% 3.55/1.32 % Negative unit clauses : 9
% 3.55/1.32 % Non-unit-clauses : 625
% 3.55/1.32 % Current number of unprocessed clauses: 4815
% 3.55/1.32 % ...number of literals in the above : 30648
% 3.55/1.32 % Current number of archived formulas : 0
% 3.55/1.32 % Current number of archived clauses : 271
% 3.55/1.32 % Clause-clause subsumption calls (NU) : 257723
% 3.55/1.32 % Rec. Clause-clause subsumption calls : 58257
% 3.55/1.32 % Non-unit clause-clause subsumptions : 1627
% 3.55/1.32 % Unit Clause-clause subsumption calls : 1647
% 3.55/1.32 % Rewrite failures with RHS unbound : 0
% 3.55/1.32 % BW rewrite match attempts : 29
% 3.55/1.32 % BW rewrite match successes : 6
% 3.55/1.32 % Condensation attempts : 0
% 3.55/1.32 % Condensation successes : 0
% 3.55/1.32 % Termbank termtop insertions : 145408
% 3.55/1.32 % Search garbage collected termcells : 1651
% 3.55/1.32
% 3.55/1.32 % -------------------------------------------------
% 3.55/1.32 % User time : 0.540 s
% 3.55/1.32 % System time : 0.020 s
% 3.55/1.32 % Total time : 0.560 s
% 3.55/1.32 % Maximum resident set size: 3968 pages
% 3.55/1.32
% 3.55/1.32 % -------------------------------------------------
% 3.55/1.32 % User time : 2.677 s
% 3.55/1.32 % System time : 0.086 s
% 3.55/1.32 % Total time : 2.763 s
% 3.55/1.32 % Maximum resident set size: 4864 pages
% 3.55/1.32 % E exiting
%------------------------------------------------------------------------------