%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP631+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 : n012.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 04:26:37 PM UTC 2026
% Result : Theorem 5.70s 4.28s
% Output : CNFRefutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 205 ( 53 equ)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 265 ( 94 ~; 97 |; 50 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 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 : 49 ( 1 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t15_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))
=> ( ( k1_group_1(X1,X2,X3) = X2
| k1_group_1(X1,X3,X2) = X2 )
=> X3 = k2_group_1(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',t15_group_1) ).
fof(d3_group_1,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> ( v3_group_1(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) = X3
& k1_group_1(X1,X2,X3) = X3
& ? [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
& k1_group_1(X1,X3,X4) = X2
& k1_group_1(X1,X4,X3) = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',d3_group_1) ).
fof(t29_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,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& 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) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_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(c_0_4,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))
=> ( ( k1_group_1(X1,X2,X3) = X2
| k1_group_1(X1,X3,X2) = X2 )
=> X3 = k2_group_1(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[t15_group_1]) ).
fof(c_0_5,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> ( v3_group_1(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) = X3
& k1_group_1(X1,X2,X3) = X3
& ? [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
& k1_group_1(X1,X3,X4) = X2
& k1_group_1(X1,X4,X3) = X2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_group_1]) ).
fof(c_0_6,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,k2_group_1(X1)),k6_autgroup(X1,X2)) = k6_autgroup(X1,X2)
& 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) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t29_autgroup])]) ).
fof(c_0_7,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_8,plain,
! [X580,X581,X582] :
( ( k1_group_1(X580,X581,X582) != X581
| X582 = k2_group_1(X580)
| ~ m1_subset_1(X582,u1_struct_0(X580))
| ~ m1_subset_1(X581,u1_struct_0(X580))
| v3_struct_0(X580)
| ~ v3_group_1(X580)
| ~ v4_group_1(X580)
| ~ l1_group_1(X580) )
& ( k1_group_1(X580,X582,X581) != X581
| X582 = k2_group_1(X580)
| ~ m1_subset_1(X582,u1_struct_0(X580))
| ~ m1_subset_1(X581,u1_struct_0(X580))
| v3_struct_0(X580)
| ~ v3_group_1(X580)
| ~ v4_group_1(X580)
| ~ l1_group_1(X580) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_9,plain,
! [X761,X763,X765,X767] :
( ( m1_subset_1(esk24_1(X761),u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( k1_group_1(X761,X763,esk24_1(X761)) = X763
| ~ m1_subset_1(X763,u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( k1_group_1(X761,esk24_1(X761),X763) = X763
| ~ m1_subset_1(X763,u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( m1_subset_1(esk25_2(X761,X763),u1_struct_0(X761))
| ~ m1_subset_1(X763,u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( k1_group_1(X761,X763,esk25_2(X761,X763)) = esk24_1(X761)
| ~ m1_subset_1(X763,u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( k1_group_1(X761,esk25_2(X761,X763),X763) = esk24_1(X761)
| ~ m1_subset_1(X763,u1_struct_0(X761))
| ~ v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( m1_subset_1(esk26_2(X761,X765),u1_struct_0(X761))
| ~ m1_subset_1(X765,u1_struct_0(X761))
| v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) )
& ( k1_group_1(X761,esk26_2(X761,X765),X765) != esk26_2(X761,X765)
| k1_group_1(X761,X765,esk26_2(X761,X765)) != esk26_2(X761,X765)
| ~ m1_subset_1(X767,u1_struct_0(X761))
| k1_group_1(X761,esk26_2(X761,X765),X767) != X765
| k1_group_1(X761,X767,esk26_2(X761,X765)) != X765
| ~ m1_subset_1(X765,u1_struct_0(X761))
| v3_group_1(X761)
| v3_struct_0(X761)
| ~ l1_group_1(X761) ) ),
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])])])])]) ).
fof(c_0_10,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,k2_group_1(esk1_0)),k6_autgroup(esk1_0,esk2_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,esk2_0),k6_autgroup(esk1_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_11,plain,
! [X541,X542,X543] :
( v3_struct_0(X541)
| ~ v1_group_1(X541)
| ~ v3_group_1(X541)
| ~ v4_group_1(X541)
| ~ l1_group_1(X541)
| ~ m1_subset_1(X542,u1_struct_0(X541))
| ~ m1_subset_1(X543,u1_struct_0(X541))
| k6_autgroup(X541,k1_group_1(X541,X542,X543)) = k7_funct_2(u1_struct_0(X541),u1_struct_0(X541),u1_struct_0(X541),k6_autgroup(X541,X542),k6_autgroup(X541,X543)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( X3 = k2_group_1(X1)
| v3_struct_0(X1)
| k1_group_1(X1,X2,X3) != X2
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( k1_group_1(X1,X2,esk24_1(X1)) = X2
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( m1_subset_1(esk24_1(X1),u1_struct_0(X1))
| v3_struct_0(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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)
| 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(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,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_11]) ).
cnf(c_0_17,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( esk24_1(X1) = 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(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_24,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)
| k6_autgroup(esk1_0,k1_group_1(esk1_0,k2_group_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_25,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_17]),c_0_18]),c_0_20])]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k6_autgroup(esk1_0,k1_group_1(esk1_0,k2_group_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_27,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_14,c_0_25]),c_0_18]),c_0_20])]),c_0_22]) ).
cnf(c_0_28,plain,
( k1_group_1(X1,esk24_1(X1),X2) = X2
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k6_autgroup(esk1_0,k1_group_1(esk1_0,k2_group_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_30,negated_conjecture,
( k1_group_1(esk1_0,k2_group_1(esk1_0),X1) = X1
| ~ 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(spm,[status(thm)],[c_0_28,c_0_25]),c_0_18]),c_0_20])]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21])]) ).
cnf(c_0_32,negated_conjecture,
( k1_group_1(esk1_0,X1,k2_group_1(esk1_0)) = X1
| ~ 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(spm,[status(thm)],[c_0_13,c_0_25]),c_0_18]),c_0_20])]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP631+2 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 18:51:46 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 5.70/4.28 % Version : CSE_E---1.7
% 5.70/4.28 % Problem : theBenchmark.p
% 5.70/4.28 % SZS status Theorem for theBenchmark.p
% 5.70/4.28 % SZS output start CNFRefutation
% See solution above
% 5.70/4.29 % Total time : 3.354s
%------------------------------------------------------------------------------