%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP629+2 : 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 : n031.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 04:26:36 PM UTC 2026
% Result : Theorem 3.23s 3.01s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 148 ( 26 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 189 ( 68 ~; 61 |; 40 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-5 aty)
% Number of variables : 39 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_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_subset_1(X2,u1_struct_0(X1))
=> k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k3_group_1(X1,X2)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k2_group_1(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_autgroup) ).
fof(t23_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_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_autgroup) ).
fof(d6_group_1,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))
=> ( X3 = k3_group_1(X1,X2)
<=> ( k1_group_1(X1,X2,X3) = k2_group_1(X1)
& k1_group_1(X1,X3,X2) = k2_group_1(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',d6_group_1) ).
fof(dt_k3_group_1,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',dt_k3_group_1) ).
fof(c_0_4,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_subset_1(X2,u1_struct_0(X1))
=> k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k3_group_1(X1,X2)),k6_autgroup(X1,X2)) = k6_autgroup(X1,k2_group_1(X1)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t26_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_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t23_autgroup]) ).
fof(c_0_6,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))
=> ( X3 = k3_group_1(X1,X2)
<=> ( k1_group_1(X1,X2,X3) = k2_group_1(X1)
& k1_group_1(X1,X3,X2) = k2_group_1(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d6_group_1]) ).
fof(c_0_7,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k3_group_1]) ).
fof(c_0_8,negated_conjecture,
( ~ 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_subset_1(esk2_0,u1_struct_0(esk1_0))
& k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k3_group_1(esk1_0,esk2_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,k2_group_1(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_9,plain,
! [X765,X766,X767] :
( v3_struct_0(X765)
| ~ v1_group_1(X765)
| ~ v3_group_1(X765)
| ~ v4_group_1(X765)
| ~ l1_group_1(X765)
| ~ m1_subset_1(X766,u1_struct_0(X765))
| ~ m1_subset_1(X767,u1_struct_0(X765))
| k6_autgroup(X765,k1_group_1(X765,X766,X767)) = k7_funct_2(u1_struct_0(X765),u1_struct_0(X765),u1_struct_0(X765),k6_autgroup(X765,X766),k6_autgroup(X765,X767)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,plain,
! [X774,X775,X776] :
( ( k1_group_1(X774,X775,X776) = k2_group_1(X774)
| X776 != k3_group_1(X774,X775)
| ~ m1_subset_1(X776,u1_struct_0(X774))
| ~ m1_subset_1(X775,u1_struct_0(X774))
| v3_struct_0(X774)
| ~ v3_group_1(X774)
| ~ v4_group_1(X774)
| ~ l1_group_1(X774) )
& ( k1_group_1(X774,X776,X775) = k2_group_1(X774)
| X776 != k3_group_1(X774,X775)
| ~ m1_subset_1(X776,u1_struct_0(X774))
| ~ m1_subset_1(X775,u1_struct_0(X774))
| v3_struct_0(X774)
| ~ v3_group_1(X774)
| ~ v4_group_1(X774)
| ~ l1_group_1(X774) )
& ( k1_group_1(X774,X775,X776) != k2_group_1(X774)
| k1_group_1(X774,X776,X775) != k2_group_1(X774)
| X776 = k3_group_1(X774,X775)
| ~ m1_subset_1(X776,u1_struct_0(X774))
| ~ m1_subset_1(X775,u1_struct_0(X774))
| v3_struct_0(X774)
| ~ v3_group_1(X774)
| ~ v4_group_1(X774)
| ~ l1_group_1(X774) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X861,X862] :
( v3_struct_0(X861)
| ~ v3_group_1(X861)
| ~ v4_group_1(X861)
| ~ l1_group_1(X861)
| ~ m1_subset_1(X862,u1_struct_0(X861))
| m1_subset_1(k3_group_1(X861,X862),u1_struct_0(X861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,negated_conjecture,
k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k3_group_1(esk1_0,esk2_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,k2_group_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( v3_struct_0(X1)
| k6_autgroup(X1,k1_group_1(X1,X2,X3)) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,X2),k6_autgroup(X1,X3))
| ~ v1_group_1(X1)
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( k1_group_1(X1,X2,X3) = k2_group_1(X1)
| v3_struct_0(X1)
| X2 != k3_group_1(X1,X3)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( v3_struct_0(X1)
| m1_subset_1(k3_group_1(X1,X2),u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( k6_autgroup(esk1_0,k2_group_1(esk1_0)) != k6_autgroup(esk1_0,k1_group_1(esk1_0,k3_group_1(esk1_0,esk2_0),esk2_0))
| ~ m1_subset_1(k3_group_1(esk1_0,esk2_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_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,plain,
( k1_group_1(X1,k3_group_1(X1,X2),X2) = k2_group_1(X1)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,k3_group_1(esk1_0,X1),X1)) != k6_autgroup(esk1_0,k1_group_1(esk1_0,k3_group_1(esk1_0,esk2_0),esk2_0))
| ~ m1_subset_1(k3_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))
| ~ m1_subset_1(X1,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(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_15]),c_0_17])]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ m1_subset_1(k3_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_18])]) ).
cnf(c_0_26,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(spm,[status(thm)],[c_0_25,c_0_21]),c_0_14]),c_0_15]),c_0_17]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP629+2 : 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
% 0.16/0.33 % Computer : n031.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 18:50:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.23/3.01 % Version : CSE_E---1.7
% 3.23/3.01 % Problem : theBenchmark.p
% 3.23/3.01 % SZS status Theorem for theBenchmark.p
% 3.23/3.01 % SZS output start CNFRefutation
% See solution above
% 3.23/3.01 % Total time : 2.453s
%------------------------------------------------------------------------------