%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP641+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:26:40 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 20 unt; 0 def)
% Number of atoms : 290 ( 19 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 357 ( 132 ~; 131 |; 66 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 2 sgn 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_m1_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_group_2) ).
fof(t19_latsubgr,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(rc5_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_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(t53_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_group_2) ).
fof(dt_k2_group_1,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(d1_latsubgr,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_latsubgr) ).
fof(dt_k1_latsubgr,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsubgr) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ~ v3_struct_0(X2)
& v3_group_1(X2)
& l1_group_1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_group_2]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& m1_group_2(X2,X1) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t19_latsubgr])]) ).
fof(c_0_13,plain,
! [X122,X123] :
( ( ~ v3_struct_0(X123)
| ~ m1_group_2(X123,X122)
| v3_struct_0(X122)
| ~ v3_group_1(X122)
| ~ l1_group_1(X122) )
& ( v3_group_1(X123)
| ~ m1_group_2(X123,X122)
| v3_struct_0(X122)
| ~ v3_group_1(X122)
| ~ l1_group_1(X122) )
& ( l1_group_1(X123)
| ~ m1_group_2(X123,X122)
| v3_struct_0(X122)
| ~ v3_group_1(X122)
| ~ l1_group_1(X122) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_14,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& v1_group_1(esk2_0)
& m1_group_2(esk2_0,esk1_0)
& ~ r2_hidden(k2_group_1(esk1_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
& ~ v1_xboole_0(X2) ) ),
inference(fof_simplification,[status(thm)],[rc5_struct_0]) ).
fof(c_0_16,plain,
! [X121] :
( ~ l1_group_1(X121)
| l1_struct_0(X121) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
cnf(c_0_17,plain,
( l1_group_1(X1)
| v3_struct_0(X2)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> k2_group_1(X2) = k2_group_1(X1) ) ),
inference(fof_simplification,[status(thm)],[t53_group_2]) ).
fof(c_0_23,plain,
! [X162] :
( ( m1_subset_1(esk17_1(X162),k1_zfmisc_1(u1_struct_0(X162)))
| v3_struct_0(X162)
| ~ l1_struct_0(X162) )
& ( ~ v1_xboole_0(esk17_1(X162))
| v3_struct_0(X162)
| ~ l1_struct_0(X162) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
cnf(c_0_24,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
l1_group_1(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
cnf(c_0_26,plain,
( v3_struct_0(X2)
| ~ v3_struct_0(X1)
| ~ m1_group_2(X1,X2)
| ~ v3_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_27,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_group_1]) ).
fof(c_0_28,plain,
! [X177,X178] :
( v3_struct_0(X177)
| ~ v3_group_1(X177)
| ~ v4_group_1(X177)
| ~ l1_group_1(X177)
| ~ m1_group_2(X178,X177)
| k2_group_1(X178) = k2_group_1(X177) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_29,plain,
! [X179,X180,X181] :
( ~ r2_hidden(X179,X180)
| ~ m1_subset_1(X180,k1_zfmisc_1(X181))
| ~ v1_xboole_0(X181) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_30,plain,
( m1_subset_1(esk17_1(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
l1_struct_0(esk2_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_19]),c_0_20])]),c_0_21]) ).
fof(c_0_33,plain,
! [X170,X171] :
( ~ m1_subset_1(X170,X171)
| v1_xboole_0(X171)
| r2_hidden(X170,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_34,plain,
! [X135] : m1_subset_1(esk8_1(X135),X135),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(X2,k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) )
=> ( X2 = k1_latsubgr(X1)
<=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(X2,X3) = u1_struct_0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_latsubgr]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k1_latsubgr(X1))
& v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
& m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_k1_latsubgr]) ).
fof(c_0_37,plain,
! [X120] :
( v3_struct_0(X120)
| ~ l1_group_1(X120)
| m1_subset_1(k2_group_1(X120),u1_struct_0(X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])]) ).
cnf(c_0_38,plain,
( v3_struct_0(X1)
| k2_group_1(X2) = k2_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
m1_subset_1(esk17_1(esk2_0),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_42,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
m1_subset_1(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_44,plain,
! [X113,X114,X115] :
( ( X114 != k1_latsubgr(X113)
| ~ v1_group_1(X115)
| ~ m1_group_2(X115,X113)
| k1_funct_1(X114,X115) = u1_struct_0(X115)
| ~ v1_funct_1(X114)
| ~ v1_funct_2(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| ~ m2_relset_1(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| v3_struct_0(X113)
| ~ v3_group_1(X113)
| ~ v4_group_1(X113)
| ~ l1_group_1(X113) )
& ( v1_group_1(esk3_2(X113,X114))
| X114 = k1_latsubgr(X113)
| ~ v1_funct_1(X114)
| ~ v1_funct_2(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| ~ m2_relset_1(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| v3_struct_0(X113)
| ~ v3_group_1(X113)
| ~ v4_group_1(X113)
| ~ l1_group_1(X113) )
& ( m1_group_2(esk3_2(X113,X114),X113)
| X114 = k1_latsubgr(X113)
| ~ v1_funct_1(X114)
| ~ v1_funct_2(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| ~ m2_relset_1(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| v3_struct_0(X113)
| ~ v3_group_1(X113)
| ~ v4_group_1(X113)
| ~ l1_group_1(X113) )
& ( k1_funct_1(X114,esk3_2(X113,X114)) != u1_struct_0(esk3_2(X113,X114))
| X114 = k1_latsubgr(X113)
| ~ v1_funct_1(X114)
| ~ v1_funct_2(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| ~ m2_relset_1(X114,k1_group_3(X113),k1_zfmisc_1(u1_struct_0(X113)))
| v3_struct_0(X113)
| ~ v3_group_1(X113)
| ~ v4_group_1(X113)
| ~ l1_group_1(X113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])]) ).
fof(c_0_45,plain,
! [X119] :
( ( v1_funct_1(k1_latsubgr(X119))
| v3_struct_0(X119)
| ~ v3_group_1(X119)
| ~ v4_group_1(X119)
| ~ l1_group_1(X119) )
& ( v1_funct_2(k1_latsubgr(X119),k1_group_3(X119),k1_zfmisc_1(u1_struct_0(X119)))
| v3_struct_0(X119)
| ~ v3_group_1(X119)
| ~ v4_group_1(X119)
| ~ l1_group_1(X119) )
& ( m2_relset_1(k1_latsubgr(X119),k1_group_3(X119),k1_zfmisc_1(u1_struct_0(X119)))
| v3_struct_0(X119)
| ~ v3_group_1(X119)
| ~ v4_group_1(X119)
| ~ l1_group_1(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
cnf(c_0_46,plain,
( v3_struct_0(X1)
| m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
k2_group_1(esk2_0) = k2_group_1(esk1_0),
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_38,c_0_18]),c_0_19]),c_0_39]),c_0_20])]),c_0_21]) ).
cnf(c_0_48,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(esk2_0))
| ~ r2_hidden(X1,esk17_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( v1_xboole_0(X1)
| r2_hidden(esk8_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( k1_funct_1(X1,X3) = u1_struct_0(X3)
| v3_struct_0(X2)
| X1 != k1_latsubgr(X2)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X2)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_relset_1(X1,k1_group_3(X2),k1_zfmisc_1(u1_struct_0(X2)))
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( v1_funct_1(k1_latsubgr(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( v1_funct_2(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
( m2_relset_1(k1_latsubgr(X1),k1_group_3(X1),k1_zfmisc_1(u1_struct_0(X1)))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,negated_conjecture,
m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_47]),c_0_32]) ).
cnf(c_0_55,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(esk17_1(X1))
| ~ l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_56,negated_conjecture,
( v1_xboole_0(esk17_1(esk2_0))
| ~ v1_xboole_0(u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,plain,
( k1_funct_1(k1_latsubgr(X1),X2) = u1_struct_0(X2)
| v3_struct_0(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X2)
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_50]),c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_58,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_59,negated_conjecture,
( v1_xboole_0(u1_struct_0(esk2_0))
| r2_hidden(k2_group_1(esk1_0),u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_31])]),c_0_32]) ).
cnf(c_0_61,negated_conjecture,
~ r2_hidden(k2_group_1(esk1_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_62,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = u1_struct_0(esk2_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_18]),c_0_58]),c_0_19]),c_0_39]),c_0_20])]),c_0_21]) ).
cnf(c_0_63,negated_conjecture,
r2_hidden(k2_group_1(esk1_0),u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP641+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 18:53:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------