%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP618+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 : n008.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 04:26:31 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 260 ( 92 ~; 95 |; 37 &)
% ( 2 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 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 : 46 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t1_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) )
<=> v1_group_3(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_autgroup) ).
fof(l2_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( v1_group_3(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_autgroup) ).
fof(l1_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) )
=> v1_group_3(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_autgroup) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) )
<=> v1_group_3(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t1_autgroup])]) ).
fof(c_0_4,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( v1_group_3(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[l2_autgroup]) ).
fof(c_0_5,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( m1_subset_1(X4,u1_struct_0(X2))
=> r1_rlvect_1(X2,k2_group_3(X1,X4,X3)) ) ) )
=> v1_group_3(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[l1_autgroup]) ).
fof(c_0_6,negated_conjecture,
! [X116,X117] :
( ~ v3_struct_0(esk1_0)
& v1_group_1(esk1_0)
& v3_group_1(esk1_0)
& v4_group_1(esk1_0)
& l1_group_1(esk1_0)
& m1_group_2(esk2_0,esk1_0)
& ( m1_subset_1(esk3_0,u1_struct_0(esk1_0))
| ~ v1_group_3(esk2_0,esk1_0) )
& ( m1_subset_1(esk4_0,u1_struct_0(esk1_0))
| ~ v1_group_3(esk2_0,esk1_0) )
& ( m1_subset_1(esk4_0,u1_struct_0(esk2_0))
| ~ v1_group_3(esk2_0,esk1_0) )
& ( ~ r1_rlvect_1(esk2_0,k2_group_3(esk1_0,esk4_0,esk3_0))
| ~ v1_group_3(esk2_0,esk1_0) )
& ( ~ m1_subset_1(X116,u1_struct_0(esk1_0))
| ~ m1_subset_1(X117,u1_struct_0(esk1_0))
| ~ m1_subset_1(X117,u1_struct_0(esk2_0))
| r1_rlvect_1(esk2_0,k2_group_3(esk1_0,X117,X116))
| v1_group_3(esk2_0,esk1_0) ) ),
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_3])])])])]) ).
fof(c_0_7,plain,
! [X216,X217,X218,X219] :
( v3_struct_0(X216)
| ~ v1_group_1(X216)
| ~ v3_group_1(X216)
| ~ v4_group_1(X216)
| ~ l1_group_1(X216)
| ~ m1_group_2(X217,X216)
| ~ v1_group_3(X217,X216)
| ~ m1_subset_1(X218,u1_struct_0(X216))
| ~ m1_subset_1(X219,u1_struct_0(X216))
| ~ m1_subset_1(X219,u1_struct_0(X217))
| r1_rlvect_1(X217,k2_group_3(X216,X219,X218)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X212,X213] :
( ( m1_subset_1(esk26_2(X212,X213),u1_struct_0(X212))
| v1_group_3(X213,X212)
| ~ m1_group_2(X213,X212)
| v3_struct_0(X212)
| ~ v1_group_1(X212)
| ~ v3_group_1(X212)
| ~ v4_group_1(X212)
| ~ l1_group_1(X212) )
& ( m1_subset_1(esk27_2(X212,X213),u1_struct_0(X212))
| v1_group_3(X213,X212)
| ~ m1_group_2(X213,X212)
| v3_struct_0(X212)
| ~ v1_group_1(X212)
| ~ v3_group_1(X212)
| ~ v4_group_1(X212)
| ~ l1_group_1(X212) )
& ( m1_subset_1(esk27_2(X212,X213),u1_struct_0(X213))
| v1_group_3(X213,X212)
| ~ m1_group_2(X213,X212)
| v3_struct_0(X212)
| ~ v1_group_1(X212)
| ~ v3_group_1(X212)
| ~ v4_group_1(X212)
| ~ l1_group_1(X212) )
& ( ~ r1_rlvect_1(X213,k2_group_3(X212,esk27_2(X212,X213),esk26_2(X212,X213)))
| v1_group_3(X213,X212)
| ~ m1_group_2(X213,X212)
| v3_struct_0(X212)
| ~ v1_group_1(X212)
| ~ v3_group_1(X212)
| ~ v4_group_1(X212)
| ~ l1_group_1(X212) ) ),
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_5])])])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ r1_rlvect_1(esk2_0,k2_group_3(esk1_0,esk4_0,esk3_0))
| ~ v1_group_3(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( v3_struct_0(X1)
| r1_rlvect_1(X2,k2_group_3(X1,X4,X3))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_3(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X2)) ),
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,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
v1_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]) ).
cnf(c_0_17,negated_conjecture,
( m1_subset_1(esk3_0,u1_struct_0(esk1_0))
| ~ v1_group_3(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( m1_subset_1(esk4_0,u1_struct_0(esk1_0))
| ~ v1_group_3(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( m1_subset_1(esk4_0,u1_struct_0(esk2_0))
| ~ v1_group_3(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( v1_group_3(X1,X2)
| v3_struct_0(X2)
| ~ r1_rlvect_1(X1,k2_group_3(X2,esk27_2(X2,X1),esk26_2(X2,X1)))
| ~ m1_group_2(X1,X2)
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( r1_rlvect_1(esk2_0,k2_group_3(esk1_0,X2,X1))
| v1_group_3(esk2_0,esk1_0)
| ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
~ v1_group_3(esk2_0,esk1_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[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_9,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]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( ~ m1_subset_1(esk27_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk27_2(esk1_0,esk2_0),u1_struct_0(esk2_0))
| ~ m1_subset_1(esk26_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
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_20,c_0_21]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]),c_0_22]) ).
cnf(c_0_24,plain,
( m1_subset_1(esk27_2(X1,X2),u1_struct_0(X2))
| v1_group_3(X2,X1)
| v3_struct_0(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( ~ m1_subset_1(esk27_2(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(esk26_2(esk1_0,esk2_0),u1_struct_0(esk1_0)) ),
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_23,c_0_24]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_22]),c_0_16]) ).
cnf(c_0_26,plain,
( m1_subset_1(esk26_2(X1,X2),u1_struct_0(X1))
| v1_group_3(X2,X1)
| v3_struct_0(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
~ m1_subset_1(esk27_2(esk1_0,esk2_0),u1_struct_0(esk1_0)),
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_25,c_0_26]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_22]),c_0_16]) ).
cnf(c_0_28,plain,
( m1_subset_1(esk27_2(X1,X2),u1_struct_0(X1))
| v1_group_3(X2,X1)
| v3_struct_0(X1)
| ~ m1_group_2(X2,X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,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_27,c_0_28]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_22]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP618+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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:46:13 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------