%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:40:29 PM UTC 2026
% Result : Theorem 0.26s 0.57s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 28 unt; 0 def)
% Number of atoms : 346 ( 19 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 411 ( 138 ~; 129 |; 92 &)
% ( 5 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 124 ( 4 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_latsubgr,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X3,X1,X2)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X3) )
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X1)
=> ! [X6] :
( m1_group_2(X6,X2)
=> ! [X7] :
( m1_group_2(X7,X2)
=> ( ( m1_group_6(X4,X1,X5)
& u1_struct_0(X7) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X5))
& u1_struct_0(X6) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X4)) )
=> m1_group_6(X6,X2,X7) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_latsubgr) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_k2_funct_2,axiom,
! [X1,X2,X3,X4] :
( ( m1_relset_1(X3,X1,X2)
& v1_funct_2(X3,X1,X2)
& v1_funct_1(X3) )
=> k2_funct_2(X1,X2,X3,X4) = k9_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_funct_2) ).
fof(t156_relat_1,axiom,
! [X1,X2,X3] :
( v1_relat_1(X3)
=> ( r1_tarski(X1,X2)
=> r1_tarski(k9_relat_1(X3,X1),k9_relat_1(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t156_relat_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> v1_relat_1(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_m1_group_6,axiom,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
<=> m1_group_2(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m1_group_6) ).
fof(t66_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> ( r1_tarski(u1_struct_0(X2),u1_struct_0(X3))
=> m1_group_2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_group_2) ).
fof(d5_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ( m1_group_2(X2,X1)
<=> ( u1_group_1(X2) = k1_realset1(u1_group_1(X1),u1_struct_0(X2))
& r1_tarski(u1_struct_0(X2),u1_struct_0(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_group_2) ).
fof(dt_m1_group_2,axiom,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( l1_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X3,X1,X2)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X3) )
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X1)
=> ! [X6] :
( m1_group_2(X6,X2)
=> ! [X7] :
( m1_group_2(X7,X2)
=> ( ( m1_group_6(X4,X1,X5)
& u1_struct_0(X7) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X5))
& u1_struct_0(X6) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X4)) )
=> m1_group_6(X6,X2,X7) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t10_latsubgr]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v4_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( m2_relset_1(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_group_6(X3,X1,X2)
& v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))
& v1_funct_1(X3) )
=> ! [X4] :
( m1_group_2(X4,X1)
=> ! [X5] :
( m1_group_2(X5,X1)
=> ! [X6] :
( m1_group_2(X6,X2)
=> ! [X7] :
( m1_group_2(X7,X2)
=> ( ( m1_group_6(X4,X1,X5)
& u1_struct_0(X7) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X5))
& u1_struct_0(X6) = k2_funct_2(u1_struct_0(X1),u1_struct_0(X2),X3,u1_struct_0(X4)) )
=> m1_group_6(X6,X2,X7) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_12,plain,
! [X86,X87,X88] :
( ( m2_relset_1(X88,X86,X87)
| ~ m1_relset_1(X88,X86,X87) )
& ( m1_relset_1(X88,X86,X87)
| ~ m2_relset_1(X88,X86,X87) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_13,negated_conjecture,
( ~ m1_group_6(esk6_0,esk2_0,esk7_0)
& m1_group_6(esk4_0,esk1_0,esk5_0)
& u1_struct_0(esk7_0) = k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,u1_struct_0(esk5_0))
& u1_struct_0(esk6_0) = k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,u1_struct_0(esk4_0))
& m1_group_2(esk7_0,esk2_0)
& m1_group_2(esk6_0,esk2_0)
& m1_group_2(esk5_0,esk1_0)
& m1_group_2(esk4_0,esk1_0)
& m2_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))
& v1_group_6(esk3_0,esk1_0,esk2_0)
& v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))
& v1_funct_1(esk3_0)
& l1_group_1(esk2_0)
& v4_group_1(esk2_0)
& v3_group_1(esk2_0)
& ~ v3_struct_0(esk2_0)
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_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_11])])])]) ).
fof(c_0_14,plain,
! [X79,X80,X81,X82] :
( k2_funct_2(X79,X80,X81,X82) = k9_relat_1(X81,X82)
| ~ m1_relset_1(X81,X79,X80)
| ~ v1_funct_2(X81,X79,X80)
| ~ v1_funct_1(X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_funct_2])])]) ).
cnf(c_0_15,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
m2_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X90,X91,X92] :
( r1_tarski(k9_relat_1(X92,X90),k9_relat_1(X92,X91))
| ~ r1_tarski(X90,X91)
| ~ v1_relat_1(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t156_relat_1])])]) ).
cnf(c_0_18,negated_conjecture,
u1_struct_0(esk6_0) = k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,u1_struct_0(esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ m1_relset_1(X1,X2,X3)
| ~ v1_funct_2(X1,X2,X3)
| ~ v1_funct_1(X1)
| k2_funct_2(X2,X3,X1,X4) = k9_relat_1(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
v1_funct_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
m1_relset_1(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_23,plain,
! [X20,X21,X22] :
( v1_relat_1(X22)
| ~ m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X20,X21))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])]) ).
fof(c_0_24,plain,
! [X41,X42,X43] :
( m1_subset_1(X43,k1_zfmisc_1(k2_zfmisc_1(X41,X42)))
| ~ m2_relset_1(X43,X41,X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])])]) ).
cnf(c_0_25,plain,
( ~ r1_tarski(X2,X3)
| ~ v1_relat_1(X1)
| r1_tarski(k9_relat_1(X1,X2),k9_relat_1(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
k9_relat_1(esk3_0,u1_struct_0(esk4_0)) = u1_struct_0(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
u1_struct_0(esk7_0) = k2_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,u1_struct_0(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,plain,
( ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,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_24]) ).
fof(c_0_30,plain,
! [X1,X2] :
( ( m1_group_2(X2,X1)
& l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X3] :
( m1_group_6(X3,X1,X2)
<=> m1_group_2(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m1_group_6]) ).
fof(c_0_31,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> ( r1_tarski(u1_struct_0(X2),u1_struct_0(X3))
=> m1_group_2(X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t66_group_2]) ).
cnf(c_0_32,negated_conjecture,
( ~ v1_relat_1(esk3_0)
| ~ r1_tarski(u1_struct_0(esk4_0),X1)
| r1_tarski(u1_struct_0(esk6_0),k9_relat_1(esk3_0,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
k9_relat_1(esk3_0,u1_struct_0(esk5_0)) = u1_struct_0(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_20]),c_0_21])]),c_0_22])]) ).
cnf(c_0_34,plain,
( ~ m2_relset_1(X1,X2,X3)
| v1_relat_1(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_35,plain,
! [X83,X84,X85] :
( ( ~ m1_group_2(X84,X83)
| ~ l1_group_1(X83)
| ~ v4_group_1(X83)
| ~ v3_group_1(X83)
| v3_struct_0(X83)
| m1_group_6(X85,X83,X84)
| ~ m1_group_2(X85,X84) )
& ( ~ m1_group_2(X84,X83)
| ~ l1_group_1(X83)
| ~ v4_group_1(X83)
| ~ v3_group_1(X83)
| v3_struct_0(X83)
| m1_group_2(X85,X84)
| ~ m1_group_6(X85,X83,X84) ) ),
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_30])])])])]) ).
fof(c_0_36,plain,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) )
=> ( m1_group_2(X2,X1)
<=> ( u1_group_1(X2) = k1_realset1(u1_group_1(X1),u1_struct_0(X2))
& r1_tarski(u1_struct_0(X2),u1_struct_0(X1)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d5_group_2]) ).
fof(c_0_37,plain,
! [X1] :
( ( l1_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( l1_group_1(X2)
& v3_group_1(X2)
& ~ v3_struct_0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_group_2]) ).
fof(c_0_38,plain,
! [X105,X106,X107] :
( m1_group_2(X106,X107)
| ~ r1_tarski(u1_struct_0(X106),u1_struct_0(X107))
| ~ m1_group_2(X107,X105)
| ~ m1_group_2(X106,X105)
| ~ l1_group_1(X105)
| ~ v4_group_1(X105)
| ~ v3_group_1(X105)
| v3_struct_0(X105) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ v1_relat_1(esk3_0)
| ~ r1_tarski(u1_struct_0(esk4_0),u1_struct_0(esk5_0))
| r1_tarski(u1_struct_0(esk6_0),u1_struct_0(esk7_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
v1_relat_1(esk3_0),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_41,negated_conjecture,
~ m1_group_6(esk6_0,esk2_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_42,plain,
( ~ m1_group_2(X2,X3)
| ~ l1_group_1(X3)
| ~ v4_group_1(X3)
| ~ v3_group_1(X3)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X3)
| m1_group_6(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
m1_group_2(esk7_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_44,negated_conjecture,
l1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
v4_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_46,negated_conjecture,
v3_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_47,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_48,plain,
! [X29,X30] :
( ( ~ l1_group_1(X29)
| ~ v3_group_1(X29)
| v3_struct_0(X29)
| ~ l1_group_1(X30)
| ~ v3_group_1(X30)
| v3_struct_0(X30)
| m1_group_2(X30,X29)
| u1_group_1(X30) != k1_realset1(u1_group_1(X29),u1_struct_0(X30))
| ~ r1_tarski(u1_struct_0(X30),u1_struct_0(X29)) )
& ( ~ l1_group_1(X29)
| ~ v3_group_1(X29)
| v3_struct_0(X29)
| ~ l1_group_1(X30)
| ~ v3_group_1(X30)
| v3_struct_0(X30)
| ~ m1_group_2(X30,X29)
| u1_group_1(X30) = k1_realset1(u1_group_1(X29),u1_struct_0(X30)) )
& ( ~ l1_group_1(X29)
| ~ v3_group_1(X29)
| v3_struct_0(X29)
| ~ l1_group_1(X30)
| ~ v3_group_1(X30)
| v3_struct_0(X30)
| ~ m1_group_2(X30,X29)
| r1_tarski(u1_struct_0(X30),u1_struct_0(X29)) ) ),
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_36])])])])]) ).
fof(c_0_49,plain,
! [X36,X37] :
( ( ~ l1_group_1(X36)
| ~ v3_group_1(X36)
| v3_struct_0(X36)
| ~ m1_group_2(X37,X36)
| l1_group_1(X37) )
& ( ~ l1_group_1(X36)
| ~ v3_group_1(X36)
| v3_struct_0(X36)
| ~ m1_group_2(X37,X36)
| v3_group_1(X37) )
& ( ~ l1_group_1(X36)
| ~ v3_group_1(X36)
| v3_struct_0(X36)
| ~ m1_group_2(X37,X36)
| ~ v3_struct_0(X37) ) ),
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_37])])])])]) ).
cnf(c_0_50,plain,
( ~ r1_tarski(u1_struct_0(X2),u1_struct_0(X3))
| ~ m1_group_2(X3,X1)
| ~ m1_group_2(X2,X1)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| m1_group_2(X2,X3)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,negated_conjecture,
( ~ r1_tarski(u1_struct_0(esk4_0),u1_struct_0(esk5_0))
| r1_tarski(u1_struct_0(esk6_0),u1_struct_0(esk7_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_52,negated_conjecture,
~ m1_group_2(esk6_0,esk7_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_41,c_0_42]),c_0_43]),c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_53,plain,
( ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,plain,
( ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| v3_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
( ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( ~ l1_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_2(X1,X2)
| ~ v3_struct_0(X1)
| v3_struct_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( ~ m1_group_2(X3,X2)
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ m1_group_6(X1,X2,X3)
| v3_struct_0(X2)
| m1_group_2(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_58,negated_conjecture,
m1_group_6(esk4_0,esk1_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_59,negated_conjecture,
m1_group_2(esk5_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_60,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_61,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_62,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_63,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_64,negated_conjecture,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(esk6_0,X1)
| ~ m1_group_2(esk7_0,X1)
| ~ r1_tarski(u1_struct_0(esk4_0),u1_struct_0(esk5_0))
| v3_struct_0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_65,plain,
( ~ v3_group_1(X2)
| ~ l1_group_1(X2)
| ~ m1_group_2(X1,X2)
| v3_struct_0(X2)
| r1_tarski(u1_struct_0(X1),u1_struct_0(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56]) ).
cnf(c_0_66,negated_conjecture,
m1_group_2(esk4_0,esk5_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_57,c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62])]),c_0_63]) ).
cnf(c_0_67,negated_conjecture,
l1_group_1(esk5_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_59]),c_0_60]),c_0_62])]),c_0_63]) ).
cnf(c_0_68,negated_conjecture,
v3_group_1(esk5_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_59]),c_0_60]),c_0_62])]),c_0_63]) ).
cnf(c_0_69,negated_conjecture,
~ v3_struct_0(esk5_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_59]),c_0_60]),c_0_62])]),c_0_63]) ).
cnf(c_0_70,negated_conjecture,
( ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(esk6_0,X1)
| ~ m1_group_2(esk7_0,X1)
| v3_struct_0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]),c_0_68])]),c_0_69]) ).
cnf(c_0_71,negated_conjecture,
m1_group_2(esk6_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_72,negated_conjecture,
$false,
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_70,c_0_45]),c_0_43]),c_0_71]),c_0_44]),c_0_46])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP637+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 20:25:00 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.57 % Version: 3.5.1
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.57 % Starting sh5l with 300s (1) cores
% 0.26/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2525009 completed with status 0
% 0.26/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.57 % No SInE strategy applied
% 0.26/0.57 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.26/0.57 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.26/0.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.26/0.57 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.26/0.57 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2525018 completed with status 0
% 0.26/0.57 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.26/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.26/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.26/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.57 % No SInE strategy applied
% 0.26/0.57 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.26/0.57 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.26/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.26/0.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.26/0.57 % Preprocessing time : 0.003 s
% 0.26/0.57
% 0.26/0.57 % Proof found!
% 0.26/0.57 % SZS status Theorem
% 0.26/0.57 % SZS output start CNFRefutation
% See solution above
% 0.26/0.57 % Parsed axioms : 55
% 0.26/0.57 % Removed by relevancy pruning/SinE : 0
% 0.26/0.57 % Initial clauses : 98
% 0.26/0.57 % Removed in clause preprocessing : 14
% 0.26/0.57 % Initial clauses in saturation : 84
% 0.26/0.57 % Processed clauses : 249
% 0.26/0.57 % ...of these trivial : 2
% 0.26/0.57 % ...subsumed : 32
% 0.26/0.57 % ...remaining for further processing : 215
% 0.26/0.57 % Other redundant clauses eliminated : 0
% 0.26/0.57 % Clauses deleted for lack of memory : 0
% 0.26/0.57 % Backward-subsumed : 7
% 0.26/0.57 % Backward-rewritten : 8
% 0.26/0.57 % Generated clauses : 318
% 0.26/0.57 % ...of the previous two non-redundant : 270
% 0.26/0.57 % ...aggressively subsumed : 0
% 0.26/0.57 % Contextual simplify-reflections : 10
% 0.26/0.57 % Paramodulations : 318
% 0.26/0.57 % Factorizations : 0
% 0.26/0.57 % NegExts : 0
% 0.26/0.57 % Equation resolutions : 0
% 0.26/0.57 % Disequality decompositions : 0
% 0.26/0.57 % Total rewrite steps : 293
% 0.26/0.57 % ...of those cached : 248
% 0.26/0.57 % Propositional unsat checks : 0
% 0.26/0.57 % Propositional check models : 0
% 0.26/0.57 % Propositional check unsatisfiable : 0
% 0.26/0.57 % Propositional clauses : 0
% 0.26/0.57 % Propositional clauses after purity: 0
% 0.26/0.57 % Propositional unsat core size : 0
% 0.26/0.57 % Propositional preprocessing time : 0.000
% 0.26/0.57 % Propositional encoding time : 0.000
% 0.26/0.57 % Propositional solver time : 0.000
% 0.26/0.57 % Success case prop preproc time : 0.000
% 0.26/0.57 % Success case prop encoding time : 0.000
% 0.26/0.57 % Success case prop solver time : 0.000
% 0.26/0.57 % Current number of processed clauses : 200
% 0.26/0.57 % Positive orientable unit clauses : 71
% 0.26/0.57 % Positive unorientable unit clauses: 0
% 0.26/0.57 % Negative unit clauses : 28
% 0.26/0.57 % Non-unit-clauses : 101
% 0.26/0.57 % Current number of unprocessed clauses: 100
% 0.26/0.57 % ...number of literals in the above : 388
% 0.26/0.57 % Current number of archived formulas : 0
% 0.26/0.57 % Current number of archived clauses : 15
% 0.26/0.57 % Clause-clause subsumption calls (NU) : 4469
% 0.26/0.57 % Rec. Clause-clause subsumption calls : 1063
% 0.26/0.57 % Non-unit clause-clause subsumptions : 23
% 0.26/0.57 % Unit Clause-clause subsumption calls : 1215
% 0.26/0.57 % Rewrite failures with RHS unbound : 0
% 0.26/0.57 % BW rewrite match attempts : 4
% 0.26/0.57 % BW rewrite match successes : 3
% 0.26/0.57 % Condensation attempts : 0
% 0.26/0.57 % Condensation successes : 0
% 0.26/0.57 % Termbank termtop insertions : 11352
% 0.26/0.57 % Search garbage collected termcells : 1190
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.022 s
% 0.26/0.57 % System time : 0.011 s
% 0.26/0.57 % Total time : 0.033 s
% 0.26/0.57 % Maximum resident set size: 3688 pages
% 0.26/0.57
% 0.26/0.57 % -------------------------------------------------
% 0.26/0.57 % User time : 0.101 s
% 0.26/0.57 % System time : 0.033 s
% 0.26/0.57 % Total time : 0.134 s
% 0.26/0.57 % Maximum resident set size: 4608 pages
% 0.26/0.57 % E exiting
%------------------------------------------------------------------------------