%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP645+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 : n001.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 04:26:42 PM UTC 2026
% Result : Theorem 1.30s 1.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 243 ( 22 equ)
% Maximal formula atoms : 38 ( 6 avg)
% Number of connectives : 320 ( 113 ~; 115 |; 68 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t24_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) )
=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_latsubgr) ).
fof(t23_latsubgr,axiom,
! [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) )
=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsubgr) ).
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(dt_k9_group_2,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_group_2(X2,X1)
& m1_group_2(X3,X1) )
=> ( v1_group_1(k9_group_2(X1,X2,X3))
& m1_group_2(k9_group_2(X1,X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_group_2) ).
fof(c_0_5,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) )
=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> k1_funct_1(k1_latsubgr(X1),k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t24_latsubgr])]) ).
fof(c_0_6,plain,
! [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) )
=> ! [X3] :
( ( v1_group_1(X3)
& m1_group_2(X3,X1) )
=> u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t23_latsubgr]) ).
fof(c_0_7,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_8,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_9,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)
& v1_group_1(esk3_0)
& m1_group_2(esk3_0,esk1_0)
& k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,plain,
! [X203,X204,X205] :
( v3_struct_0(X203)
| ~ v3_group_1(X203)
| ~ v4_group_1(X203)
| ~ l1_group_1(X203)
| ~ v1_group_1(X204)
| ~ m1_group_2(X204,X203)
| ~ v1_group_1(X205)
| ~ m1_group_2(X205,X203)
| u1_struct_0(k9_group_2(X203,X204,X205)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X203),X204),k1_funct_1(k1_latsubgr(X203),X205)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_11,plain,
! [X137,X138,X139] :
( ( X138 != k1_latsubgr(X137)
| ~ v1_group_1(X139)
| ~ m1_group_2(X139,X137)
| k1_funct_1(X138,X139) = u1_struct_0(X139)
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| ~ m2_relset_1(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| v3_struct_0(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) )
& ( v1_group_1(esk4_2(X137,X138))
| X138 = k1_latsubgr(X137)
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| ~ m2_relset_1(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| v3_struct_0(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) )
& ( m1_group_2(esk4_2(X137,X138),X137)
| X138 = k1_latsubgr(X137)
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| ~ m2_relset_1(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| v3_struct_0(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) )
& ( k1_funct_1(X138,esk4_2(X137,X138)) != u1_struct_0(esk4_2(X137,X138))
| X138 = k1_latsubgr(X137)
| ~ v1_funct_1(X138)
| ~ v1_funct_2(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| ~ m2_relset_1(X138,k1_group_3(X137),k1_zfmisc_1(u1_struct_0(X137)))
| v3_struct_0(X137)
| ~ v3_group_1(X137)
| ~ v4_group_1(X137)
| ~ l1_group_1(X137) ) ),
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_7])])])])]) ).
fof(c_0_12,plain,
! [X143] :
( ( v1_funct_1(k1_latsubgr(X143))
| v3_struct_0(X143)
| ~ v3_group_1(X143)
| ~ v4_group_1(X143)
| ~ l1_group_1(X143) )
& ( v1_funct_2(k1_latsubgr(X143),k1_group_3(X143),k1_zfmisc_1(u1_struct_0(X143)))
| v3_struct_0(X143)
| ~ v3_group_1(X143)
| ~ v4_group_1(X143)
| ~ l1_group_1(X143) )
& ( m2_relset_1(k1_latsubgr(X143),k1_group_3(X143),k1_zfmisc_1(u1_struct_0(X143)))
| v3_struct_0(X143)
| ~ v3_group_1(X143)
| ~ v4_group_1(X143)
| ~ l1_group_1(X143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != k3_xboole_0(k1_funct_1(k1_latsubgr(esk1_0),esk2_0),k1_funct_1(k1_latsubgr(esk1_0),esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( v3_struct_0(X1)
| u1_struct_0(k9_group_2(X1,X2,X3)) = k3_xboole_0(k1_funct_1(k1_latsubgr(X1),X2),k1_funct_1(k1_latsubgr(X1),X3))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
m1_group_2(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
v1_group_1(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,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_11]) ).
cnf(c_0_24,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_12]) ).
cnf(c_0_25,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_12]) ).
cnf(c_0_26,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_12]) ).
fof(c_0_27,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_group_2(X2,X1)
& m1_group_2(X3,X1) )
=> ( v1_group_1(k9_group_2(X1,X2,X3))
& m1_group_2(k9_group_2(X1,X2,X3),X1) ) ),
inference(fof_simplification,[status(thm)],[dt_k9_group_2]) ).
cnf(c_0_28,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),k9_group_2(esk1_0,esk2_0,esk3_0)) != u1_struct_0(k9_group_2(esk1_0,esk2_0,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_29,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(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]) ).
fof(c_0_30,plain,
! [X147,X148,X149] :
( ( v1_group_1(k9_group_2(X147,X148,X149))
| v3_struct_0(X147)
| ~ v3_group_1(X147)
| ~ v4_group_1(X147)
| ~ l1_group_1(X147)
| ~ m1_group_2(X148,X147)
| ~ m1_group_2(X149,X147) )
& ( m1_group_2(k9_group_2(X147,X148,X149),X147)
| v3_struct_0(X147)
| ~ v3_group_1(X147)
| ~ v4_group_1(X147)
| ~ l1_group_1(X147)
| ~ m1_group_2(X148,X147)
| ~ m1_group_2(X149,X147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_31,negated_conjecture,
( ~ m1_group_2(k9_group_2(esk1_0,esk2_0,esk3_0),esk1_0)
| ~ v1_group_1(k9_group_2(esk1_0,esk2_0,esk3_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_28,c_0_29]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_32,plain,
( m1_group_2(k9_group_2(X1,X2,X3),X1)
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ v1_group_1(k9_group_2(esk1_0,esk2_0,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_15]),c_0_16]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_34,plain,
( v1_group_1(k9_group_2(X1,X2,X3))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_group_2(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_15]),c_0_16]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP645+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n001.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:55:03 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Theorem for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.30/1.74 % Total time : 1.373s
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