%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP631+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:27 PM UTC 2026
% Result : Theorem 50.04s 7.97s
% Output : CNFRefutation 50.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 19 unt; 0 def)
% Number of atoms : 220 ( 57 equ)
% Maximal formula atoms : 43 ( 5 avg)
% Number of connectives : 268 ( 91 ~; 96 |; 55 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-5 aty)
% Number of variables : 53 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t29_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_autgroup) ).
fof(d3_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v3_group_1(X1)
<=> ? [X2] :
( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ? [X4] :
( k1_group_1(X1,X4,X3) = X2
& k1_group_1(X1,X3,X4) = X2
& m1_subset_1(X4,u1_struct_0(X1)) )
& k1_group_1(X1,X2,X3) = X3
& k1_group_1(X1,X3,X2) = X3 ) )
& m1_subset_1(X2,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',d3_group_1) ).
fof(t15_group_1,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( k1_group_1(X1,X3,X2) = X2
| k1_group_1(X1,X2,X3) = X2 )
=> X3 = k2_group_1(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',t15_group_1) ).
fof(t23_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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(c_0_4,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t29_autgroup]) ).
fof(c_0_5,plain,
! [X1] :
( ( l1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ( v3_group_1(X1)
<=> ? [X2] :
( ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ? [X4] :
( k1_group_1(X1,X4,X3) = X2
& k1_group_1(X1,X3,X4) = X2
& m1_subset_1(X4,u1_struct_0(X1)) )
& k1_group_1(X1,X2,X3) = X3
& k1_group_1(X1,X3,X2) = X3 ) )
& m1_subset_1(X2,u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[d3_group_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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,X2),k6_autgroup(X1,k2_group_1(X1))) = k6_autgroup(X1,X2)
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( ( k1_group_1(X1,X3,X2) = X2
| k1_group_1(X1,X2,X3) = X2 )
=> X3 = k2_group_1(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[t15_group_1]) ).
fof(c_0_8,plain,
! [X305,X307,X309,X311] :
( ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| v3_group_1(X305)
| ~ m1_subset_1(X309,u1_struct_0(X305))
| k1_group_1(X305,X311,esk26_2(X305,X309)) != X309
| k1_group_1(X305,esk26_2(X305,X309),X311) != X309
| ~ m1_subset_1(X311,u1_struct_0(X305))
| k1_group_1(X305,X309,esk26_2(X305,X309)) != esk26_2(X305,X309)
| k1_group_1(X305,esk26_2(X305,X309),X309) != esk26_2(X305,X309) )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| v3_group_1(X305)
| ~ m1_subset_1(X309,u1_struct_0(X305))
| m1_subset_1(esk26_2(X305,X309),u1_struct_0(X305)) )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| ~ m1_subset_1(X307,u1_struct_0(X305))
| k1_group_1(X305,esk25_2(X305,X307),X307) = esk24_1(X305) )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| ~ m1_subset_1(X307,u1_struct_0(X305))
| k1_group_1(X305,X307,esk25_2(X305,X307)) = esk24_1(X305) )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| ~ m1_subset_1(X307,u1_struct_0(X305))
| m1_subset_1(esk25_2(X305,X307),u1_struct_0(X305)) )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| ~ m1_subset_1(X307,u1_struct_0(X305))
| k1_group_1(X305,esk24_1(X305),X307) = X307 )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| ~ m1_subset_1(X307,u1_struct_0(X305))
| k1_group_1(X305,X307,esk24_1(X305)) = X307 )
& ( ~ l1_group_1(X305)
| v3_struct_0(X305)
| ~ v3_group_1(X305)
| m1_subset_1(esk24_1(X305),u1_struct_0(X305)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).
fof(c_0_9,negated_conjecture,
( ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0) )
& m1_subset_1(esk2_0,u1_struct_0(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X78,X79,X80] :
( ( ~ l1_group_1(X78)
| ~ v4_group_1(X78)
| ~ v3_group_1(X78)
| v3_struct_0(X78)
| ~ m1_subset_1(X79,u1_struct_0(X78))
| ~ m1_subset_1(X80,u1_struct_0(X78))
| X80 = k2_group_1(X78)
| k1_group_1(X78,X80,X79) != X79 )
& ( ~ l1_group_1(X78)
| ~ v4_group_1(X78)
| ~ v3_group_1(X78)
| v3_struct_0(X78)
| ~ m1_subset_1(X79,u1_struct_0(X78))
| ~ m1_subset_1(X80,u1_struct_0(X78))
| X80 = k2_group_1(X78)
| k1_group_1(X78,X79,X80) != X79 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_11,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,X2,esk24_1(X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1))
| k1_group_1(X1,X2,X3) != X2
| v3_struct_0(X1)
| X3 = k2_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
k1_group_1(esk1_0,esk2_0,esk24_1(esk1_0)) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_18,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ m1_subset_1(esk24_1(esk1_0),u1_struct_0(esk1_0))
| esk24_1(esk1_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_13]),c_0_14]),c_0_12])]),c_0_15]) ).
cnf(c_0_20,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| v3_struct_0(X1)
| m1_subset_1(esk24_1(X1),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_21,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(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]) ).
cnf(c_0_22,negated_conjecture,
esk24_1(esk1_0) = k2_group_1(esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]),c_0_14])]),c_0_15]) ).
fof(c_0_23,plain,
! [X22,X23,X24] :
( k6_autgroup(X22,k1_group_1(X22,X23,X24)) = k7_funct_2(u1_struct_0(X22),u1_struct_0(X22),u1_struct_0(X22),k6_autgroup(X22,X23),k6_autgroup(X22,X24))
| ~ m1_subset_1(X24,u1_struct_0(X22))
| ~ m1_subset_1(X23,u1_struct_0(X22))
| ~ l1_group_1(X22)
| ~ v4_group_1(X22)
| ~ v3_group_1(X22)
| ~ v1_group_1(X22)
| v3_struct_0(X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_24,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| m1_subset_1(esk25_2(X1,X2),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_26,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,X2,esk25_2(X1,X2)) = esk24_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
( ~ l1_group_1(X1)
| ~ v3_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| v3_struct_0(X1)
| k1_group_1(X1,esk24_1(X1),X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(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))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
m1_subset_1(esk25_2(esk1_0,k2_group_1(esk1_0)),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_31,negated_conjecture,
k1_group_1(esk1_0,k2_group_1(esk1_0),esk25_2(esk1_0,k2_group_1(esk1_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_26,c_0_25]),c_0_22]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_32,negated_conjecture,
k1_group_1(esk1_0,esk24_1(esk1_0),esk2_0) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ m1_subset_1(X1,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,X1),k6_autgroup(esk1_0,esk2_0)) = k6_autgroup(esk1_0,k1_group_1(esk1_0,X1,esk2_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_28,c_0_12]),c_0_18]),c_0_13]),c_0_29]),c_0_14])]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk25_2(esk1_0,esk25_2(esk1_0,k2_group_1(esk1_0))),u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_35,negated_conjecture,
esk25_2(esk1_0,k2_group_1(esk1_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_18]),c_0_13]),c_0_14]),c_0_30]),c_0_25])]),c_0_15]) ).
cnf(c_0_36,negated_conjecture,
k1_group_1(esk1_0,k2_group_1(esk1_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_37,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) = k6_autgroup(esk1_0,esk2_0),
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_33,c_0_34]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( ~ m1_subset_1(X1,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,X1),k6_autgroup(esk1_0,k2_group_1(esk1_0))) = k6_autgroup(esk1_0,k1_group_1(esk1_0,X1,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(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_28,c_0_34]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_18]),c_0_13]),c_0_29]),c_0_14])]),c_0_15]) ).
cnf(c_0_40,negated_conjecture,
k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0)) = esk2_0,
inference(rw,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_41,negated_conjecture,
k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_autgroup(esk1_0,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_12]),c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP631+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n012.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sun Sep 20 20:21:52 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.42 Running first-order theorem proving
% 0.08/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.04/7.97 % Version: 3.5.1
% 50.04/7.97 % Preprocessing class: FMLMSMMLSSSNFFN.
% 50.04/7.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.04/7.97 % Starting new_bool_3 with 900s (3) cores
% 50.04/7.97 % Starting new_bool_1 with 900s (3) cores
% 50.04/7.97 % Starting sh5l with 300s (1) cores
% 50.04/7.97 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S032N with 300s (1) cores
% 50.04/7.97 % new_bool_3 with pid 794597 completed with status 0
% 50.04/7.97 % Result found by new_bool_3
% 50.04/7.97 % Preprocessing class: FMLMSMMLSSSNFFN.
% 50.04/7.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.04/7.97 % Starting new_bool_3 with 900s (3) cores
% 50.04/7.97 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 50.04/7.97 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 50.04/7.97 % Search class: FGHSM-SMLM32-MFFFFFNN
% 50.04/7.97 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 50.04/7.97 % Starting SubtermCWHack with 82s (1) cores
% 50.04/7.97 % Starting new_bool_3 with 91s (1) cores
% 50.04/7.97 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 50.04/7.97 % new_bool_3 with pid 794603 completed with status 0
% 50.04/7.97 % Result found by new_bool_3
% 50.04/7.97 % Preprocessing class: FMLMSMMLSSSNFFN.
% 50.04/7.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.04/7.97 % Starting new_bool_3 with 900s (3) cores
% 50.04/7.97 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 50.04/7.97 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 50.04/7.97 % Search class: FGHSM-SMLM32-MFFFFFNN
% 50.04/7.97 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 50.04/7.97 % Starting SubtermCWHack with 82s (1) cores
% 50.04/7.97 % Starting new_bool_3 with 91s (1) cores
% 50.04/7.97 % Preprocessing time : 0.037 s
% 50.04/7.97 % Presaturation interreduction done
% 50.04/7.97
% 50.04/7.97 % Proof found!
% 50.04/7.97 % SZS status Theorem
% 50.04/7.97 % SZS output start CNFRefutation
% See solution above
% 50.04/7.97 % Parsed axioms : 3844
% 50.04/7.97 % Removed by relevancy pruning/SinE : 2982
% 50.04/7.97 % Initial clauses : 1741
% 50.04/7.97 % Removed in clause preprocessing : 70
% 50.04/7.97 % Initial clauses in saturation : 1671
% 50.04/7.97 % Processed clauses : 20597
% 50.04/7.97 % ...of these trivial : 567
% 50.04/7.97 % ...subsumed : 12288
% 50.04/7.97 % ...remaining for further processing : 7742
% 50.04/7.97 % Other redundant clauses eliminated : 1517
% 50.04/7.97 % Clauses deleted for lack of memory : 0
% 50.04/7.97 % Backward-subsumed : 126
% 50.04/7.97 % Backward-rewritten : 307
% 50.04/7.97 % Generated clauses : 235803
% 50.04/7.97 % ...of the previous two non-redundant : 222077
% 50.04/7.97 % ...aggressively subsumed : 0
% 50.04/7.97 % Contextual simplify-reflections : 130
% 50.04/7.97 % Paramodulations : 234209
% 50.04/7.97 % Factorizations : 30
% 50.04/7.97 % NegExts : 0
% 50.04/7.97 % Equation resolutions : 1576
% 50.04/7.97 % Disequality decompositions : 0
% 50.04/7.97 % Total rewrite steps : 153770
% 50.04/7.97 % ...of those cached : 151806
% 50.04/7.97 % Propositional unsat checks : 1
% 50.04/7.97 % Propositional check models : 0
% 50.04/7.97 % Propositional check unsatisfiable : 0
% 50.04/7.97 % Propositional clauses : 0
% 50.04/7.97 % Propositional clauses after purity: 0
% 50.04/7.97 % Propositional unsat core size : 0
% 50.04/7.97 % Propositional preprocessing time : 0.000
% 50.04/7.97 % Propositional encoding time : 0.088
% 50.04/7.97 % Propositional solver time : 0.096
% 50.04/7.97 % Success case prop preproc time : 0.000
% 50.04/7.97 % Success case prop encoding time : 0.000
% 50.04/7.97 % Success case prop solver time : 0.000
% 50.04/7.97 % Current number of processed clauses : 5590
% 50.04/7.97 % Positive orientable unit clauses : 915
% 50.04/7.97 % Positive unorientable unit clauses: 2
% 50.04/7.97 % Negative unit clauses : 975
% 50.04/7.97 % Non-unit-clauses : 3698
% 50.04/7.97 % Current number of unprocessed clauses: 204158
% 50.04/7.97 % ...number of literals in the above : 711163
% 50.04/7.97 % Current number of archived formulas : 0
% 50.04/7.97 % Current number of archived clauses : 1986
% 50.04/7.97 % Clause-clause subsumption calls (NU) : 4027664
% 50.04/7.97 % Rec. Clause-clause subsumption calls : 1148620
% 50.04/7.97 % Non-unit clause-clause subsumptions : 4995
% 50.04/7.97 % Unit Clause-clause subsumption calls : 371625
% 50.04/7.97 % Rewrite failures with RHS unbound : 0
% 50.04/7.97 % BW rewrite match attempts : 2134
% 50.04/7.97 % BW rewrite match successes : 198
% 50.04/7.97 % Condensation attempts : 0
% 50.04/7.97 % Condensation successes : 0
% 50.04/7.97 % Termbank termtop insertions : 5030118
% 50.04/7.97 % Search garbage collected termcells : 57009
% 50.04/7.97
% 50.04/7.97 % -------------------------------------------------
% 50.04/7.97 % User time : 6.870 s
% 50.04/7.97 % System time : 0.242 s
% 50.04/7.97 % Total time : 7.113 s
% 50.04/7.97 % Maximum resident set size: 14256 pages
% 50.04/7.97
% 50.04/7.97 % -------------------------------------------------
% 50.04/7.97 % User time : 20.730 s
% 50.04/7.97 % System time : 0.589 s
% 50.04/7.97 % Total time : 21.319 s
% 50.04/7.97 % Maximum resident set size: 9472 pages
% 50.04/7.97 % E exiting
%------------------------------------------------------------------------------