%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP642+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 5.32s 4.83s
% Output : CNFRefutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 68 ( 9 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 74 ( 26 ~; 15 |; 23 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d1_xboole_0) ).
fof(t19_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) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_latsubgr) ).
fof(t20_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) )
=> k1_funct_1(k1_latsubgr(X1),X2) != k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_latsubgr) ).
fof(c_0_3,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_4,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) )
=> r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2)) ) ),
inference(fof_simplification,[status(thm)],[t19_latsubgr]) ).
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) )
=> k1_funct_1(k1_latsubgr(X1),X2) != k1_xboole_0 ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t20_latsubgr])]) ).
fof(c_0_6,plain,
! [X1313,X1314,X1315] :
( ( X1313 != k1_xboole_0
| ~ r2_hidden(X1314,X1313) )
& ( r2_hidden(esk3_1(X1315),X1315)
| X1315 = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
fof(c_0_7,plain,
! [X1440,X1441] :
( v3_struct_0(X1440)
| ~ v3_group_1(X1440)
| ~ v4_group_1(X1440)
| ~ l1_group_1(X1440)
| ~ v1_group_1(X1441)
| ~ m1_group_2(X1441,X1440)
| r2_hidden(k2_group_1(X1440),k1_funct_1(k1_latsubgr(X1440),X1441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,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)
& k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = k1_xboole_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( X1 != k1_xboole_0
| ~ r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( v3_struct_0(X1)
| r2_hidden(k2_group_1(X1),k1_funct_1(k1_latsubgr(X1),X2))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X1) ),
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_8]) ).
cnf(c_0_12,negated_conjecture,
k1_funct_1(k1_latsubgr(esk1_0),esk2_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
v1_group_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP642+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:53:31 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 5.32/4.83 % Version : CSE_E---1.7
% 5.32/4.83 % Problem : theBenchmark.p
% 5.32/4.83 % SZS status Theorem for theBenchmark.p
% 5.32/4.83 % SZS output start CNFRefutation
% See solution above
% 5.32/4.84 % Total time : 4.196s
%------------------------------------------------------------------------------