%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP628+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 : n028.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 04:26:35 PM UTC 2026
% Result : Theorem 15.08s 12.05s
% Output : CNFRefutation 15.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 23 unt; 0 def)
% Number of atoms : 375 ( 42 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 486 ( 175 ~; 176 |; 89 &)
% ( 2 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& v1_group_3(X2,k3_autgroup(X1))
& m1_group_2(X2,k3_autgroup(X1)) )
=> ( X2 = k5_autgroup(X1)
<=> u1_struct_0(X2) = k4_autgroup(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_autgroup) ).
fof(dt_k5_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_group_1(k5_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& m1_group_2(k5_autgroup(X1),k3_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_autgroup) ).
fof(t57_group_2,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_group_2(X3,X1)
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X3))
=> ( X4 = X2
=> k3_group_1(X3,X4) = k3_group_1(X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t57_group_2) ).
fof(t51_group_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+246.ax',t51_group_2) ).
fof(t22_autgroup,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k5_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k5_autgroup(X1),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_autgroup) ).
fof(dt_k3_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( ~ v3_struct_0(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& l1_group_1(k3_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_autgroup) ).
fof(t11_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_autgroup) ).
fof(t13_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(c_0_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_group_1(X2)
& v1_group_3(X2,k3_autgroup(X1))
& m1_group_2(X2,k3_autgroup(X1)) )
=> ( X2 = k5_autgroup(X1)
<=> u1_struct_0(X2) = k4_autgroup(X1) ) ) ),
inference(fof_simplification,[status(thm)],[d5_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) )
=> ( v1_group_1(k5_autgroup(X1))
& v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
& m1_group_2(k5_autgroup(X1),k3_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k5_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_group_2(X3,X1)
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X3))
=> ( X4 = X2
=> k3_group_1(X3,X4) = k3_group_1(X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t57_group_2]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m1_group_2(X2,X1)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> m1_subset_1(X3,u1_struct_0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[t51_group_2]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k5_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k5_autgroup(X1),X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t22_autgroup])]) ).
fof(c_0_13,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( ~ v3_struct_0(k3_autgroup(X1))
& v1_group_1(k3_autgroup(X1))
& v3_group_1(k3_autgroup(X1))
& v4_group_1(k3_autgroup(X1))
& l1_group_1(k3_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_autgroup]) ).
fof(c_0_14,plain,
! [X2134,X2135] :
( ( X2135 != k5_autgroup(X2134)
| u1_struct_0(X2135) = k4_autgroup(X2134)
| ~ v1_group_1(X2135)
| ~ v1_group_3(X2135,k3_autgroup(X2134))
| ~ m1_group_2(X2135,k3_autgroup(X2134))
| v3_struct_0(X2134)
| ~ v1_group_1(X2134)
| ~ v3_group_1(X2134)
| ~ v4_group_1(X2134)
| ~ l1_group_1(X2134) )
& ( u1_struct_0(X2135) != k4_autgroup(X2134)
| X2135 = k5_autgroup(X2134)
| ~ v1_group_1(X2135)
| ~ v1_group_3(X2135,k3_autgroup(X2134))
| ~ m1_group_2(X2135,k3_autgroup(X2134))
| v3_struct_0(X2134)
| ~ v1_group_1(X2134)
| ~ v3_group_1(X2134)
| ~ v4_group_1(X2134)
| ~ l1_group_1(X2134) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_15,plain,
! [X2133] :
( ( v1_group_1(k5_autgroup(X2133))
| v3_struct_0(X2133)
| ~ v1_group_1(X2133)
| ~ v3_group_1(X2133)
| ~ v4_group_1(X2133)
| ~ l1_group_1(X2133) )
& ( v1_group_3(k5_autgroup(X2133),k3_autgroup(X2133))
| v3_struct_0(X2133)
| ~ v1_group_1(X2133)
| ~ v3_group_1(X2133)
| ~ v4_group_1(X2133)
| ~ l1_group_1(X2133) )
& ( m1_group_2(k5_autgroup(X2133),k3_autgroup(X2133))
| v3_struct_0(X2133)
| ~ v1_group_1(X2133)
| ~ v3_group_1(X2133)
| ~ v4_group_1(X2133)
| ~ l1_group_1(X2133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_16,plain,
! [X2100,X2101,X2102,X2103] :
( v3_struct_0(X2100)
| ~ v3_group_1(X2100)
| ~ v4_group_1(X2100)
| ~ l1_group_1(X2100)
| ~ m1_subset_1(X2101,u1_struct_0(X2100))
| ~ m1_group_2(X2102,X2100)
| ~ m1_subset_1(X2103,u1_struct_0(X2102))
| X2103 != X2101
| k3_group_1(X2102,X2103) = k3_group_1(X2100,X2101) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X2517,X2518,X2519] :
( v3_struct_0(X2517)
| ~ v3_group_1(X2517)
| ~ l1_group_1(X2517)
| ~ m1_group_2(X2518,X2517)
| ~ m1_subset_1(X2519,u1_struct_0(X2518))
| m1_subset_1(X2519,u1_struct_0(X2517)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_18,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)
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0)))
& esk2_0 = esk3_0
& k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_19,plain,
! [X2669] :
( ( ~ v3_struct_0(k3_autgroup(X2669))
| v3_struct_0(X2669)
| ~ v1_group_1(X2669)
| ~ v3_group_1(X2669)
| ~ v4_group_1(X2669)
| ~ l1_group_1(X2669) )
& ( v1_group_1(k3_autgroup(X2669))
| v3_struct_0(X2669)
| ~ v1_group_1(X2669)
| ~ v3_group_1(X2669)
| ~ v4_group_1(X2669)
| ~ l1_group_1(X2669) )
& ( v3_group_1(k3_autgroup(X2669))
| v3_struct_0(X2669)
| ~ v1_group_1(X2669)
| ~ v3_group_1(X2669)
| ~ v4_group_1(X2669)
| ~ l1_group_1(X2669) )
& ( v4_group_1(k3_autgroup(X2669))
| v3_struct_0(X2669)
| ~ v1_group_1(X2669)
| ~ v3_group_1(X2669)
| ~ v4_group_1(X2669)
| ~ l1_group_1(X2669) )
& ( l1_group_1(k3_autgroup(X2669))
| v3_struct_0(X2669)
| ~ v1_group_1(X2669)
| ~ v3_group_1(X2669)
| ~ v4_group_1(X2669)
| ~ l1_group_1(X2669) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_20,plain,
( u1_struct_0(X1) = k4_autgroup(X2)
| v3_struct_0(X2)
| X1 != k5_autgroup(X2)
| ~ v1_group_1(X1)
| ~ v1_group_3(X1,k3_autgroup(X2))
| ~ m1_group_2(X1,k3_autgroup(X2))
| ~ v1_group_1(X2)
| ~ v3_group_1(X2)
| ~ v4_group_1(X2)
| ~ l1_group_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( v1_group_1(k5_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( m1_group_2(k5_autgroup(X1),k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( v1_group_3(k5_autgroup(X1),k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( v3_struct_0(X1)
| k3_group_1(X3,X4) = k3_group_1(X1,X2)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_group_2(X3,X1)
| ~ m1_subset_1(X4,u1_struct_0(X3))
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( v3_struct_0(X1)
| m1_subset_1(X3,u1_struct_0(X1))
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_group_2(X2,X1)
| ~ m1_subset_1(X3,u1_struct_0(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_30,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,plain,
( v4_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,plain,
( v3_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_33,plain,
( l1_group_1(k3_autgroup(X1))
| v3_struct_0(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_34,plain,
( u1_struct_0(k5_autgroup(X1)) = k4_autgroup(X1)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ l1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_35,plain,
( v3_struct_0(X1)
| ~ v3_struct_0(k3_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_36,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
=> ( X2 = X3
=> k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t11_autgroup]) ).
fof(c_0_37,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[t13_autgroup]) ).
cnf(c_0_38,plain,
( k3_group_1(X1,X2) = k3_group_1(X3,X2)
| v3_struct_0(X1)
| ~ m1_group_2(X3,X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ l1_group_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_39,negated_conjecture,
m1_group_2(k5_autgroup(esk1_0),k3_autgroup(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_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_40,negated_conjecture,
v4_group_1(k3_autgroup(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_31,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_41,negated_conjecture,
v3_group_1(k3_autgroup(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_32,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_42,negated_conjecture,
l1_group_1(k3_autgroup(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_33,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_43,negated_conjecture,
u1_struct_0(k5_autgroup(esk1_0)) = k4_autgroup(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_34,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_44,negated_conjecture,
~ v3_struct_0(k3_autgroup(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_35,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_45,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k5_autgroup(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_46,plain,
! [X2676,X2677,X2678] :
( v3_struct_0(X2676)
| ~ v1_group_1(X2676)
| ~ v3_group_1(X2676)
| ~ v4_group_1(X2676)
| ~ l1_group_1(X2676)
| ~ m2_fraenkel(X2677,u1_struct_0(X2676),u1_struct_0(X2676),k1_autgroup(X2676))
| ~ m1_subset_1(X2678,u1_struct_0(k3_autgroup(X2676)))
| X2677 != X2678
| k2_funct_1(X2677) = k3_group_1(k3_autgroup(X2676),X2678) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_47,plain,
! [X2242,X2243] :
( v3_struct_0(X2242)
| ~ v1_group_1(X2242)
| ~ v3_group_1(X2242)
| ~ v4_group_1(X2242)
| ~ l1_group_1(X2242)
| ~ m2_fraenkel(X2243,u1_struct_0(X2242),u1_struct_0(X2242),k4_autgroup(X2242))
| m2_fraenkel(X2243,u1_struct_0(X2242),u1_struct_0(X2242),k1_autgroup(X2242)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_48,negated_conjecture,
m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_49,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,negated_conjecture,
k2_funct_1(esk2_0) != k3_group_1(k5_autgroup(esk1_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,negated_conjecture,
( k3_group_1(k5_autgroup(esk1_0),X1) = k3_group_1(k3_autgroup(esk1_0),X1)
| ~ m1_subset_1(X1,k4_autgroup(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_38,c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_52,negated_conjecture,
m1_subset_1(esk3_0,k4_autgroup(esk1_0)),
inference(rw,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_53,plain,
( v3_struct_0(X1)
| k2_funct_1(X2) = k3_group_1(k3_autgroup(X1),X3)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m1_subset_1(X3,u1_struct_0(k3_autgroup(X1)))
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
( v3_struct_0(X1)
| m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(k3_autgroup(esk1_0)))
| ~ m1_subset_1(X1,u1_struct_0(k5_autgroup(esk1_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_41]),c_0_42])]),c_0_44]) ).
cnf(c_0_57,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk3_0) != k2_funct_1(esk3_0),
inference(rw,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
k3_group_1(k5_autgroup(esk1_0),esk3_0) = k3_group_1(k3_autgroup(esk1_0),esk3_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( k3_group_1(k3_autgroup(X1),X2) = k2_funct_1(X2)
| v3_struct_0(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ l1_group_1(X1)
| ~ m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ m1_subset_1(X2,u1_struct_0(k3_autgroup(X1))) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k1_autgroup(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_54,c_0_55]),c_0_27]),c_0_28]),c_0_29]),c_0_26])]),c_0_30]) ).
cnf(c_0_61,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k3_autgroup(esk1_0))),
inference(spm,[status(thm)],[c_0_56,c_0_45]) ).
cnf(c_0_62,negated_conjecture,
k3_group_1(k3_autgroup(esk1_0),esk3_0) != k2_funct_1(esk3_0),
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_59,c_0_60]),c_0_27]),c_0_28]),c_0_29]),c_0_26]),c_0_61])]),c_0_62]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP628+3 : 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
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:49:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 15.08/12.05 % Version : CSE_E---1.7
% 15.08/12.05 % Problem : theBenchmark.p
% 15.08/12.05 % SZS status Theorem for theBenchmark.p
% 15.08/12.05 % SZS output start CNFRefutation
% See solution above
% 15.08/12.08 % Total time : 10.591s
%------------------------------------------------------------------------------