%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP631+3 : 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 : n022.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 22.73s 16.33s
% Output : CNFRefutation 22.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 8 unt; 0 def)
% Number of atoms : 335 ( 81 equ)
% Maximal formula atoms : 56 ( 8 avg)
% Number of connectives : 460 ( 166 ~; 174 |; 88 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-5 aty)
% Number of variables : 70 ( 0 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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_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,
~ ! [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,
! [X914,X915,X916] :
( ( k1_group_1(X914,X915,X916) = k2_group_1(X914)
| X916 != k3_group_1(X914,X915)
| ~ m1_subset_1(X916,u1_struct_0(X914))
| ~ m1_subset_1(X915,u1_struct_0(X914))
| v3_struct_0(X914)
| ~ v3_group_1(X914)
| ~ v4_group_1(X914)
| ~ l1_group_1(X914) )
& ( k1_group_1(X914,X916,X915) = k2_group_1(X914)
| X916 != k3_group_1(X914,X915)
| ~ m1_subset_1(X916,u1_struct_0(X914))
| ~ m1_subset_1(X915,u1_struct_0(X914))
| v3_struct_0(X914)
| ~ v3_group_1(X914)
| ~ v4_group_1(X914)
| ~ l1_group_1(X914) )
& ( k1_group_1(X914,X915,X916) != k2_group_1(X914)
| k1_group_1(X914,X916,X915) != k2_group_1(X914)
| X916 = k3_group_1(X914,X915)
| ~ m1_subset_1(X916,u1_struct_0(X914))
| ~ m1_subset_1(X915,u1_struct_0(X914))
| v3_struct_0(X914)
| ~ v3_group_1(X914)
| ~ v4_group_1(X914)
| ~ l1_group_1(X914) ) ),
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_10,plain,
! [X957,X958] :
( v3_struct_0(X957)
| ~ v3_group_1(X957)
| ~ v4_group_1(X957)
| ~ l1_group_1(X957)
| ~ m1_subset_1(X958,u1_struct_0(X957))
| m1_subset_1(k3_group_1(X957,X958),u1_struct_0(X957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_11,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_12,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_13,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])])]) ).
cnf(c_0_14,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_9]) ).
cnf(c_0_15,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_10]) ).
fof(c_0_16,plain,
! [X972,X973,X974] :
( ( k1_group_1(X972,k1_group_1(X972,X973,X974),k3_group_1(X972,X974)) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,k1_group_1(X972,X973,k3_group_1(X972,X974)),X974) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,k1_group_1(X972,k3_group_1(X972,X974),X974),X973) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,k1_group_1(X972,X974,k3_group_1(X972,X974)),X973) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,X973,k1_group_1(X972,X974,k3_group_1(X972,X974))) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,X973,k1_group_1(X972,k3_group_1(X972,X974),X974)) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,k3_group_1(X972,X974),k1_group_1(X972,X974,X973)) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) )
& ( k1_group_1(X972,X974,k1_group_1(X972,k3_group_1(X972,X974),X973)) = X973
| ~ m1_subset_1(X974,u1_struct_0(X972))
| ~ m1_subset_1(X973,u1_struct_0(X972))
| v3_struct_0(X972)
| ~ v3_group_1(X972)
| ~ v4_group_1(X972)
| ~ l1_group_1(X972) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,plain,
! [X844,X846,X848,X850] :
( ( m1_subset_1(esk26_1(X844),u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( k1_group_1(X844,X846,esk26_1(X844)) = X846
| ~ m1_subset_1(X846,u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( k1_group_1(X844,esk26_1(X844),X846) = X846
| ~ m1_subset_1(X846,u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( m1_subset_1(esk27_2(X844,X846),u1_struct_0(X844))
| ~ m1_subset_1(X846,u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( k1_group_1(X844,X846,esk27_2(X844,X846)) = esk26_1(X844)
| ~ m1_subset_1(X846,u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( k1_group_1(X844,esk27_2(X844,X846),X846) = esk26_1(X844)
| ~ m1_subset_1(X846,u1_struct_0(X844))
| ~ v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( m1_subset_1(esk28_2(X844,X848),u1_struct_0(X844))
| ~ m1_subset_1(X848,u1_struct_0(X844))
| v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) )
& ( k1_group_1(X844,esk28_2(X844,X848),X848) != esk28_2(X844,X848)
| k1_group_1(X844,X848,esk28_2(X844,X848)) != esk28_2(X844,X848)
| ~ m1_subset_1(X850,u1_struct_0(X844))
| k1_group_1(X844,esk28_2(X844,X848),X850) != X848
| k1_group_1(X844,X850,esk28_2(X844,X848)) != X848
| ~ m1_subset_1(X848,u1_struct_0(X844))
| v3_group_1(X844)
| v3_struct_0(X844)
| ~ l1_group_1(X844) ) ),
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_12])])])])]) ).
cnf(c_0_18,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_13]) ).
cnf(c_0_19,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_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
( k1_group_1(X1,k3_group_1(X1,X2),k1_group_1(X1,X2,X3)) = X3
| v3_struct_0(X1)
| ~ 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_16]) ).
cnf(c_0_25,plain,
( k1_group_1(X1,esk26_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_17]) ).
cnf(c_0_26,plain,
( m1_subset_1(esk26_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_17]) ).
fof(c_0_27,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]) ).
cnf(c_0_28,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,k1_group_1(esk1_0,k3_group_1(esk1_0,X1),X1))) != 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,k1_group_1(esk1_0,k3_group_1(esk1_0,X1),X1)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_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_18,c_0_19]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_29,plain,
( k1_group_1(X1,k3_group_1(X1,esk26_1(X1)),X2) = X2
| 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_24,c_0_25]),c_0_26]) ).
fof(c_0_30,plain,
! [X646,X647,X648] :
( v3_struct_0(X646)
| ~ v1_group_1(X646)
| ~ v3_group_1(X646)
| ~ v4_group_1(X646)
| ~ l1_group_1(X646)
| ~ m1_subset_1(X647,u1_struct_0(X646))
| ~ m1_subset_1(X648,u1_struct_0(X646))
| k6_autgroup(X646,k1_group_1(X646,X647,X648)) = k7_funct_2(u1_struct_0(X646),u1_struct_0(X646),u1_struct_0(X646),k6_autgroup(X646,X647),k6_autgroup(X646,X648)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_31,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,esk26_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,esk26_1(esk1_0)),k6_autgroup(esk1_0,esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ m1_subset_1(esk26_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(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]),c_0_21]),c_0_22])]),c_0_23]) ).
cnf(c_0_32,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_30]) ).
cnf(c_0_33,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,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,esk26_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k6_autgroup(esk1_0,k1_group_1(esk1_0,esk26_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ m1_subset_1(esk26_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_31,c_0_32]),c_0_20]),c_0_21]),c_0_33]),c_0_22]),c_0_34])]),c_0_23]) ).
cnf(c_0_36,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,esk26_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| k6_autgroup(esk1_0,k1_group_1(esk1_0,esk26_1(esk1_0),esk2_0)) != k6_autgroup(esk1_0,esk2_0)
| ~ m1_subset_1(esk26_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_35,c_0_32]),c_0_20]),c_0_21]),c_0_33]),c_0_22]),c_0_34])]),c_0_23]) ).
cnf(c_0_37,negated_conjecture,
( k6_autgroup(esk1_0,k1_group_1(esk1_0,esk2_0,esk26_1(esk1_0))) != k6_autgroup(esk1_0,esk2_0)
| ~ m1_subset_1(esk26_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(spm,[status(thm)],[c_0_36,c_0_25]),c_0_21]),c_0_22]),c_0_34])]),c_0_23]) ).
cnf(c_0_38,plain,
( k1_group_1(X1,X2,esk26_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_17]) ).
cnf(c_0_39,negated_conjecture,
~ m1_subset_1(esk26_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(spm,[status(thm)],[c_0_37,c_0_38]),c_0_21]),c_0_22]),c_0_34])]),c_0_23]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_26]),c_0_21]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP631+3 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 18:49:52 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 22.73/16.33 % Version : CSE_E---1.7
% 22.73/16.33 % Problem : theBenchmark.p
% 22.73/16.33 % SZS status Theorem for theBenchmark.p
% 22.73/16.33 % SZS output start CNFRefutation
% See solution above
% 22.73/16.39 % Total time : 13.910s
%------------------------------------------------------------------------------