%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP631+4 : 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 04:26:37 PM UTC 2026
% Result : Theorem 62.83s 53.55s
% Output : CNFRefutation 62.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 337 ( 75 equ)
% Maximal formula atoms : 56 ( 7 avg)
% Number of connectives : 454 ( 164 ~; 166 |; 84 &)
% ( 4 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-5 aty)
% Number of variables : 80 ( 1 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t27_group_3,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))
=> ( k2_group_3(X1,X2,X3) = X2
<=> k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+252.ax',t27_group_3) ).
fof(t22_group_3,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))
=> k2_group_3(X1,k2_group_1(X1),X2) = k2_group_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+252.ax',t22_group_3) ).
fof(dt_k2_group_1,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',dt_k2_group_1) ).
fof(t1_group_3,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,k1_group_1(X1,X2,X3),k3_group_1(X1,X3)) = X2
& k1_group_1(X1,k1_group_1(X1,X2,k3_group_1(X1,X3)),X3) = X2
& k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X3),X2) = X2
& k1_group_1(X1,k1_group_1(X1,X3,k3_group_1(X1,X3)),X2) = X2
& k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
& k1_group_1(X1,X2,k1_group_1(X1,k3_group_1(X1,X3),X3)) = X2
& k1_group_1(X1,k3_group_1(X1,X3),k1_group_1(X1,X3,X2)) = X2
& k1_group_1(X1,X3,k1_group_1(X1,k3_group_1(X1,X3),X2)) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+252.ax',t1_group_3) ).
fof(c_0_8,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_9,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_10,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_11,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_12,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_8])])]) ).
fof(c_0_13,plain,
! [X747,X748,X749] :
( v3_struct_0(X747)
| ~ v1_group_1(X747)
| ~ v3_group_1(X747)
| ~ v4_group_1(X747)
| ~ l1_group_1(X747)
| ~ m1_subset_1(X748,u1_struct_0(X747))
| ~ m1_subset_1(X749,u1_struct_0(X747))
| k6_autgroup(X747,k1_group_1(X747,X748,X749)) = k7_funct_2(u1_struct_0(X747),u1_struct_0(X747),u1_struct_0(X747),k6_autgroup(X747,X748),k6_autgroup(X747,X749)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,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))
=> ( k2_group_3(X1,X2,X3) = X2
<=> k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[t27_group_3]) ).
fof(c_0_15,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))
=> k2_group_3(X1,k2_group_1(X1),X2) = k2_group_1(X1) ) ),
inference(fof_simplification,[status(thm)],[t22_group_3]) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_group_1(X1) )
=> m1_subset_1(k2_group_1(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_group_1]) ).
fof(c_0_17,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,k1_group_1(X1,X2,X3),k3_group_1(X1,X3)) = X2
& k1_group_1(X1,k1_group_1(X1,X2,k3_group_1(X1,X3)),X3) = X2
& k1_group_1(X1,k1_group_1(X1,k3_group_1(X1,X3),X3),X2) = X2
& k1_group_1(X1,k1_group_1(X1,X3,k3_group_1(X1,X3)),X2) = X2
& k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
& k1_group_1(X1,X2,k1_group_1(X1,k3_group_1(X1,X3),X3)) = X2
& k1_group_1(X1,k3_group_1(X1,X3),k1_group_1(X1,X3,X2)) = X2
& k1_group_1(X1,X3,k1_group_1(X1,k3_group_1(X1,X3),X2)) = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[t1_group_3]) ).
fof(c_0_18,plain,
! [X1052,X1053,X1054] :
( ( k1_group_1(X1052,X1053,X1054) = k2_group_1(X1052)
| X1054 != k3_group_1(X1052,X1053)
| ~ m1_subset_1(X1054,u1_struct_0(X1052))
| ~ m1_subset_1(X1053,u1_struct_0(X1052))
| v3_struct_0(X1052)
| ~ v3_group_1(X1052)
| ~ v4_group_1(X1052)
| ~ l1_group_1(X1052) )
& ( k1_group_1(X1052,X1054,X1053) = k2_group_1(X1052)
| X1054 != k3_group_1(X1052,X1053)
| ~ m1_subset_1(X1054,u1_struct_0(X1052))
| ~ m1_subset_1(X1053,u1_struct_0(X1052))
| v3_struct_0(X1052)
| ~ v3_group_1(X1052)
| ~ v4_group_1(X1052)
| ~ l1_group_1(X1052) )
& ( k1_group_1(X1052,X1053,X1054) != k2_group_1(X1052)
| k1_group_1(X1052,X1054,X1053) != k2_group_1(X1052)
| X1054 = k3_group_1(X1052,X1053)
| ~ m1_subset_1(X1054,u1_struct_0(X1052))
| ~ m1_subset_1(X1053,u1_struct_0(X1052))
| v3_struct_0(X1052)
| ~ v3_group_1(X1052)
| ~ v4_group_1(X1052)
| ~ l1_group_1(X1052) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_19,plain,
! [X1100,X1101] :
( v3_struct_0(X1100)
| ~ v3_group_1(X1100)
| ~ v4_group_1(X1100)
| ~ l1_group_1(X1100)
| ~ m1_subset_1(X1101,u1_struct_0(X1100))
| m1_subset_1(k3_group_1(X1100,X1101),u1_struct_0(X1100)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_20,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_12]) ).
cnf(c_0_21,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_13]) ).
cnf(c_0_22,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_28,plain,
! [X878,X879,X880] :
( ( k2_group_3(X878,X879,X880) != X879
| k1_group_1(X878,X879,X880) = k1_group_1(X878,X880,X879)
| ~ m1_subset_1(X880,u1_struct_0(X878))
| ~ m1_subset_1(X879,u1_struct_0(X878))
| v3_struct_0(X878)
| ~ v3_group_1(X878)
| ~ v4_group_1(X878)
| ~ l1_group_1(X878) )
& ( k1_group_1(X878,X879,X880) != k1_group_1(X878,X880,X879)
| k2_group_3(X878,X879,X880) = X879
| ~ m1_subset_1(X880,u1_struct_0(X878))
| ~ m1_subset_1(X879,u1_struct_0(X878))
| v3_struct_0(X878)
| ~ v3_group_1(X878)
| ~ v4_group_1(X878)
| ~ l1_group_1(X878) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_29,plain,
! [X867,X868] :
( v3_struct_0(X867)
| ~ v3_group_1(X867)
| ~ v4_group_1(X867)
| ~ l1_group_1(X867)
| ~ m1_subset_1(X868,u1_struct_0(X867))
| k2_group_3(X867,k2_group_1(X867),X868) = k2_group_1(X867) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_30,plain,
! [X788] :
( v3_struct_0(X788)
| ~ l1_group_1(X788)
| m1_subset_1(k2_group_1(X788),u1_struct_0(X788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_31,plain,
! [X1115,X1116,X1117] :
( ( k1_group_1(X1115,k1_group_1(X1115,X1116,X1117),k3_group_1(X1115,X1117)) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,k1_group_1(X1115,X1116,k3_group_1(X1115,X1117)),X1117) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,k1_group_1(X1115,k3_group_1(X1115,X1117),X1117),X1116) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,k1_group_1(X1115,X1117,k3_group_1(X1115,X1117)),X1116) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,X1116,k1_group_1(X1115,X1117,k3_group_1(X1115,X1117))) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,X1116,k1_group_1(X1115,k3_group_1(X1115,X1117),X1117)) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,k3_group_1(X1115,X1117),k1_group_1(X1115,X1117,X1116)) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) )
& ( k1_group_1(X1115,X1117,k1_group_1(X1115,k3_group_1(X1115,X1117),X1116)) = X1116
| ~ m1_subset_1(X1117,u1_struct_0(X1115))
| ~ m1_subset_1(X1116,u1_struct_0(X1115))
| v3_struct_0(X1115)
| ~ v3_group_1(X1115)
| ~ v4_group_1(X1115)
| ~ l1_group_1(X1115) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_32,plain,
( k1_group_1(X1,X2,X3) = k2_group_1(X1)
| v3_struct_0(X1)
| X3 != k3_group_1(X1,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_18]) ).
cnf(c_0_33,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_19]) ).
cnf(c_0_34,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_20,c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_35,plain,
( k1_group_1(X1,X2,X3) = k1_group_1(X1,X3,X2)
| v3_struct_0(X1)
| k2_group_3(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_28]) ).
cnf(c_0_36,plain,
( v3_struct_0(X1)
| k2_group_3(X1,k2_group_1(X1),X2) = k2_group_1(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_29]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| m1_subset_1(k2_group_1(X1),u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( k1_group_1(X1,X2,k1_group_1(X1,X3,k3_group_1(X1,X3))) = X2
| v3_struct_0(X1)
| ~ 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_31]) ).
cnf(c_0_39,plain,
( k1_group_1(X1,X2,k3_group_1(X1,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_32]),c_0_33]) ).
cnf(c_0_40,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_34,c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_41,plain,
( k1_group_1(X1,k2_group_1(X1),X2) = k1_group_1(X1,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(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
( k1_group_1(X1,X2,k2_group_1(X1)) = X2
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,k2_group_1(esk1_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(spm,[status(thm)],[c_0_40,c_0_41]),c_0_22]),c_0_23]),c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_44,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_22]),c_0_23]),c_0_25])]),c_0_27]) ).
cnf(c_0_45,negated_conjecture,
~ m1_subset_1(k2_group_1(esk1_0),u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_26])]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_25])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP631+4 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:50:34 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 62.83/53.55 % Version : CSE_E---1.7
% 62.83/53.55 % Problem : theBenchmark.p
% 62.83/53.55 % SZS status Theorem for theBenchmark.p
% 62.83/53.55 % SZS output start CNFRefutation
% See solution above
% 62.93/53.63 % Total time : 50.344s
%------------------------------------------------------------------------------