%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP643+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 04:26:41 PM UTC 2026
% Result : Theorem 1.14s 1.62s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 198 ( 66 ~; 59 |; 43 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t21_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] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
& r2_hidden(X4,k1_funct_1(k1_latsubgr(X1),X2)) )
=> r2_hidden(k1_group_1(X1,X3,X4),k1_funct_1(k1_latsubgr(X1),X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_latsubgr) ).
fof(t18_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] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
<=> r1_rlvect_1(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_latsubgr) ).
fof(t59_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_group_2(X4,X1)
=> ( ( r1_rlvect_1(X4,X2)
& r1_rlvect_1(X4,X3) )
=> r1_rlvect_1(X4,k1_group_1(X1,X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_group_2) ).
fof(dt_k1_group_1,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_group_1) ).
fof(c_0_4,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] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
& r2_hidden(X4,k1_funct_1(k1_latsubgr(X1),X2)) )
=> r2_hidden(k1_group_1(X1,X3,X4),k1_funct_1(k1_latsubgr(X1),X2)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t21_latsubgr])]) ).
fof(c_0_5,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] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r2_hidden(X3,k1_funct_1(k1_latsubgr(X1),X2))
<=> r1_rlvect_1(X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t18_latsubgr]) ).
fof(c_0_6,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)
& m1_subset_1(esk3_0,u1_struct_0(esk1_0))
& m1_subset_1(esk4_0,u1_struct_0(esk1_0))
& r2_hidden(esk3_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0))
& r2_hidden(esk4_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0))
& ~ r2_hidden(k1_group_1(esk1_0,esk3_0,esk4_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_4])])]) ).
fof(c_0_7,plain,
! [X174,X175,X176] :
( ( ~ r2_hidden(X176,k1_funct_1(k1_latsubgr(X174),X175))
| r1_rlvect_1(X175,X176)
| ~ m1_subset_1(X176,u1_struct_0(X174))
| ~ v1_group_1(X175)
| ~ m1_group_2(X175,X174)
| v3_struct_0(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) )
& ( ~ r1_rlvect_1(X175,X176)
| r2_hidden(X176,k1_funct_1(k1_latsubgr(X174),X175))
| ~ m1_subset_1(X176,u1_struct_0(X174))
| ~ v1_group_1(X175)
| ~ m1_group_2(X175,X174)
| v3_struct_0(X174)
| ~ v3_group_1(X174)
| ~ v4_group_1(X174)
| ~ l1_group_1(X174) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_group_2(X4,X1)
=> ( ( r1_rlvect_1(X4,X2)
& r1_rlvect_1(X4,X3) )
=> r1_rlvect_1(X4,k1_group_1(X1,X2,X3)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t59_group_2]) ).
cnf(c_0_9,negated_conjecture,
~ r2_hidden(k1_group_1(esk1_0,esk3_0,esk4_0),k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( r2_hidden(X2,k1_funct_1(k1_latsubgr(X3),X1))
| v3_struct_0(X3)
| ~ r1_rlvect_1(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X3))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X3)
| ~ v3_group_1(X3)
| ~ v4_group_1(X3)
| ~ l1_group_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_17,plain,
! [X186,X187,X188,X189] :
( v3_struct_0(X186)
| ~ v3_group_1(X186)
| ~ v4_group_1(X186)
| ~ l1_group_1(X186)
| ~ m1_subset_1(X187,u1_struct_0(X186))
| ~ m1_subset_1(X188,u1_struct_0(X186))
| ~ m1_group_2(X189,X186)
| ~ r1_rlvect_1(X189,X187)
| ~ r1_rlvect_1(X189,X188)
| r1_rlvect_1(X189,k1_group_1(X186,X187,X188)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_18,plain,
( r1_rlvect_1(X3,X1)
| v3_struct_0(X2)
| ~ r2_hidden(X1,k1_funct_1(k1_latsubgr(X2),X3))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ v1_group_1(X3)
| ~ m1_group_2(X3,X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
r2_hidden(esk4_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk4_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
r2_hidden(esk3_0,k1_funct_1(k1_latsubgr(esk1_0),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_23,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1))
& m1_subset_1(X3,u1_struct_0(X1)) )
=> m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_group_1]) ).
cnf(c_0_24,negated_conjecture,
( ~ r1_rlvect_1(esk2_0,k1_group_1(esk1_0,esk3_0,esk4_0))
| ~ m1_subset_1(k1_group_1(esk1_0,esk3_0,esk4_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_25,plain,
( v3_struct_0(X1)
| r1_rlvect_1(X4,k1_group_1(X1,X2,X3))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_group_2(X4,X1)
| ~ r1_rlvect_1(X4,X2)
| ~ r1_rlvect_1(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
r1_rlvect_1(esk2_0,esk4_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(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_27,negated_conjecture,
r1_rlvect_1(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(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
fof(c_0_28,plain,
! [X123,X124,X125] :
( v3_struct_0(X123)
| ~ l1_group_1(X123)
| ~ m1_subset_1(X124,u1_struct_0(X123))
| ~ m1_subset_1(X125,u1_struct_0(X123))
| m1_subset_1(k1_group_1(X123,X124,X125),u1_struct_0(X123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_29,negated_conjecture,
~ m1_subset_1(k1_group_1(esk1_0,esk3_0,esk4_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_20]),c_0_22]),c_0_11]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_30,plain,
( v3_struct_0(X1)
| m1_subset_1(k1_group_1(X1,X2,X3),u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
$false,
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_29,c_0_30]),c_0_20]),c_0_22]),c_0_13])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP643+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 18:54:00 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.14/1.62 % Version : CSE_E---1.7
% 1.14/1.62 % Problem : theBenchmark.p
% 1.14/1.62 % SZS status Theorem for theBenchmark.p
% 1.14/1.62 % SZS output start CNFRefutation
% See solution above
% 1.14/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------