%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP641+2 : 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 : n006.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 5.46s 4.89s
% Output : CNFRefutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 175 ( 10 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 209 ( 71 ~; 65 |; 43 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/Axioms/SET007/SET007+246.ax',t53_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/sandbox2/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(t54_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)
=> ! [X3] :
( m1_group_2(X3,X1)
=> k2_group_1(X2) = k2_group_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+246.ax',t54_group_2) ).
fof(t56_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)
=> ! [X3] :
( m1_group_2(X3,X1)
=> r1_rlvect_1(X3,k2_group_1(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+246.ax',t56_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/sandbox2/benchmark/Axioms/SET007/SET007+212.ax',dt_k2_group_1) ).
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(c_0_6,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_7,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_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> k2_group_1(X2) = k2_group_1(X3) ) ) ),
inference(fof_simplification,[status(thm)],[t54_group_2]) ).
fof(c_0_9,plain,
! [X1456,X1457] :
( v3_struct_0(X1456)
| ~ v3_group_1(X1456)
| ~ v4_group_1(X1456)
| ~ l1_group_1(X1456)
| ~ m1_group_2(X1457,X1456)
| k2_group_1(X1457) = k2_group_1(X1456) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,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_7])])]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_group_2(X3,X1)
=> r1_rlvect_1(X3,k2_group_1(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[t56_group_2]) ).
fof(c_0_12,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_13,plain,
! [X1458,X1459,X1460] :
( v3_struct_0(X1458)
| ~ v3_group_1(X1458)
| ~ v4_group_1(X1458)
| ~ l1_group_1(X1458)
| ~ m1_group_2(X1459,X1458)
| ~ m1_group_2(X1460,X1458)
| k2_group_1(X1459) = k2_group_1(X1460) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_14,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_9]) ).
cnf(c_0_15,negated_conjecture,
m1_group_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X1463,X1464,X1465] :
( v3_struct_0(X1463)
| ~ v3_group_1(X1463)
| ~ v4_group_1(X1463)
| ~ l1_group_1(X1463)
| ~ m1_group_2(X1464,X1463)
| ~ m1_group_2(X1465,X1463)
| r1_rlvect_1(X1465,k2_group_1(X1464)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_21,plain,
! [X1455] :
( v3_struct_0(X1455)
| ~ l1_group_1(X1455)
| m1_subset_1(k2_group_1(X1455),u1_struct_0(X1455)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_22,plain,
( v3_struct_0(X1)
| k2_group_1(X2) = k2_group_1(X3)
| ~ 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_13]) ).
cnf(c_0_23,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_14,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
fof(c_0_24,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]) ).
cnf(c_0_25,plain,
( v3_struct_0(X1)
| r1_rlvect_1(X3,k2_group_1(X2))
| ~ 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_20]) ).
cnf(c_0_26,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_21]) ).
cnf(c_0_27,negated_conjecture,
( k2_group_1(X1) = k2_group_1(esk1_0)
| ~ m1_group_2(X1,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_22,c_0_15]),c_0_23]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
fof(c_0_28,plain,
! [X1437,X1438,X1439] :
( ( ~ r2_hidden(X1439,k1_funct_1(k1_latsubgr(X1437),X1438))
| r1_rlvect_1(X1438,X1439)
| ~ m1_subset_1(X1439,u1_struct_0(X1437))
| ~ v1_group_1(X1438)
| ~ m1_group_2(X1438,X1437)
| v3_struct_0(X1437)
| ~ v3_group_1(X1437)
| ~ v4_group_1(X1437)
| ~ l1_group_1(X1437) )
& ( ~ r1_rlvect_1(X1438,X1439)
| r2_hidden(X1439,k1_funct_1(k1_latsubgr(X1437),X1438))
| ~ m1_subset_1(X1439,u1_struct_0(X1437))
| ~ v1_group_1(X1438)
| ~ m1_group_2(X1438,X1437)
| v3_struct_0(X1437)
| ~ v3_group_1(X1437)
| ~ v4_group_1(X1437)
| ~ l1_group_1(X1437) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_29,negated_conjecture,
( r1_rlvect_1(esk2_0,k2_group_1(X1))
| ~ m1_group_2(X1,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_25,c_0_15]),c_0_16]),c_0_17]),c_0_18])]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( m1_subset_1(k2_group_1(X1),u1_struct_0(esk1_0))
| ~ m1_group_2(X1,esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18])]),c_0_19]) ).
cnf(c_0_31,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_10]) ).
cnf(c_0_32,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_28]) ).
cnf(c_0_33,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_34,negated_conjecture,
r1_rlvect_1(esk2_0,k2_group_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_15])]) ).
cnf(c_0_35,negated_conjecture,
m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_15])]) ).
cnf(c_0_36,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(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_17]),c_0_33]),c_0_18]),c_0_34]),c_0_35])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP641+2 : TPTP v9.2.1. Released v3.4.0.
% 0.11/0.13 % 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
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 18:53:47 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.18/0.35 % start to proof: theBenchmark
% 5.46/4.89 % Version : CSE_E---1.7
% 5.46/4.89 % Problem : theBenchmark.p
% 5.46/4.89 % SZS status Theorem for theBenchmark.p
% 5.46/4.89 % SZS output start CNFRefutation
% See solution above
% 5.56/4.90 % Total time : 4.196s
%------------------------------------------------------------------------------