%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP624+1 : 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 : n003.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 04:26:34 PM UTC 2026
% Result : Theorem 3.85s 3.11s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 14 unt; 0 def)
% Number of atoms : 354 ( 23 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 463 ( 174 ~; 172 |; 81 &)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-6 aty)
% Number of variables : 123 ( 2 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(redefinition_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(dt_k1_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_fraenkel,axiom,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
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(t15_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] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_autgroup) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(d2_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_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_autgroup) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k2_autgroup,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_autgroup) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( ( ~ v1_xboole_0(X2)
& m1_fraenkel(X3,X1,X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
<=> m1_subset_1(X4,X3) ) ),
inference(fof_simplification,[status(thm)],[redefinition_m2_fraenkel]) ).
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) )
=> m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k1_autgroup]) ).
fof(c_0_14,plain,
! [X242] :
( v3_struct_0(X242)
| ~ l1_struct_0(X242)
| ~ v1_xboole_0(u1_struct_0(X242)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_15,plain,
! [X209] :
( ~ l1_group_1(X209)
| l1_struct_0(X209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_16,plain,
! [X1,X2,X3] :
( m1_fraenkel(X3,X1,X2)
=> ( ~ v1_xboole_0(X3)
& v1_fraenkel(X3) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_fraenkel]) ).
fof(c_0_17,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]) ).
fof(c_0_18,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] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> k1_binop_1(k2_autgroup(X1),X2,X3) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X3,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t15_autgroup])]) ).
fof(c_0_19,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X2)
& v1_funct_1(X4)
& v1_funct_2(X4,k2_zfmisc_1(X1,X2),X3)
& m1_relset_1(X4,k2_zfmisc_1(X1,X2),X3)
& m1_subset_1(X5,X1)
& m1_subset_1(X6,X2) )
=> k2_binop_1(X1,X2,X3,X4,X5,X6) = k1_binop_1(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1]) ).
fof(c_0_20,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ! [X2] :
( ( v1_funct_1(X2)
& v1_funct_2(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(X2,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) )
=> ( X2 = k2_autgroup(X1)
<=> ! [X3] :
( m2_fraenkel(X3,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> ! [X4] :
( m2_fraenkel(X4,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
=> k2_binop_1(k1_autgroup(X1),k1_autgroup(X1),k1_autgroup(X1),X2,X3,X4) = k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X4,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d2_autgroup]) ).
fof(c_0_21,plain,
! [X277,X278,X279,X280] :
( ( ~ m2_fraenkel(X280,X277,X278,X279)
| m1_subset_1(X280,X279)
| v1_xboole_0(X278)
| ~ m1_fraenkel(X279,X277,X278) )
& ( ~ m1_subset_1(X280,X279)
| m2_fraenkel(X280,X277,X278,X279)
| v1_xboole_0(X278)
| ~ m1_fraenkel(X279,X277,X278) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_22,plain,
! [X193] :
( v3_struct_0(X193)
| ~ v1_group_1(X193)
| ~ v3_group_1(X193)
| ~ v4_group_1(X193)
| ~ l1_group_1(X193)
| m1_fraenkel(k1_autgroup(X193),u1_struct_0(X193),u1_struct_0(X193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
cnf(c_0_23,plain,
( v3_struct_0(X1)
| ~ l1_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_25,plain,
! [X210,X211,X212] :
( ( ~ v1_xboole_0(X212)
| ~ m1_fraenkel(X212,X210,X211) )
& ( v1_fraenkel(X212)
| ~ m1_fraenkel(X212,X210,X211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_26,plain,
! [X285,X286] :
( v3_struct_0(X285)
| ~ v1_group_1(X285)
| ~ v3_group_1(X285)
| ~ v4_group_1(X285)
| ~ l1_group_1(X285)
| ~ m2_fraenkel(X286,u1_struct_0(X285),u1_struct_0(X285),k4_autgroup(X285))
| m2_fraenkel(X286,u1_struct_0(X285),u1_struct_0(X285),k1_autgroup(X285)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_27,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))
& m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_28,plain,
! [X266,X267,X268,X269,X270,X271] :
( v1_xboole_0(X266)
| v1_xboole_0(X267)
| ~ v1_funct_1(X269)
| ~ v1_funct_2(X269,k2_zfmisc_1(X266,X267),X268)
| ~ m1_relset_1(X269,k2_zfmisc_1(X266,X267),X268)
| ~ m1_subset_1(X270,X266)
| ~ m1_subset_1(X271,X267)
| k2_binop_1(X266,X267,X268,X269,X270,X271) = k1_binop_1(X269,X270,X271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
fof(c_0_29,plain,
! [X183,X184,X185,X186] :
( ( X184 != k2_autgroup(X183)
| ~ m2_fraenkel(X185,u1_struct_0(X183),u1_struct_0(X183),k1_autgroup(X183))
| ~ m2_fraenkel(X186,u1_struct_0(X183),u1_struct_0(X183),k1_autgroup(X183))
| k2_binop_1(k1_autgroup(X183),k1_autgroup(X183),k1_autgroup(X183),X184,X185,X186) = k7_funct_2(u1_struct_0(X183),u1_struct_0(X183),u1_struct_0(X183),X186,X185)
| ~ v1_funct_1(X184)
| ~ v1_funct_2(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| ~ m2_relset_1(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| v3_struct_0(X183)
| ~ v1_group_1(X183)
| ~ v3_group_1(X183)
| ~ v4_group_1(X183)
| ~ l1_group_1(X183) )
& ( m2_fraenkel(esk4_2(X183,X184),u1_struct_0(X183),u1_struct_0(X183),k1_autgroup(X183))
| X184 = k2_autgroup(X183)
| ~ v1_funct_1(X184)
| ~ v1_funct_2(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| ~ m2_relset_1(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| v3_struct_0(X183)
| ~ v1_group_1(X183)
| ~ v3_group_1(X183)
| ~ v4_group_1(X183)
| ~ l1_group_1(X183) )
& ( m2_fraenkel(esk5_2(X183,X184),u1_struct_0(X183),u1_struct_0(X183),k1_autgroup(X183))
| X184 = k2_autgroup(X183)
| ~ v1_funct_1(X184)
| ~ v1_funct_2(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| ~ m2_relset_1(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| v3_struct_0(X183)
| ~ v1_group_1(X183)
| ~ v3_group_1(X183)
| ~ v4_group_1(X183)
| ~ l1_group_1(X183) )
& ( k2_binop_1(k1_autgroup(X183),k1_autgroup(X183),k1_autgroup(X183),X184,esk4_2(X183,X184),esk5_2(X183,X184)) != k7_funct_2(u1_struct_0(X183),u1_struct_0(X183),u1_struct_0(X183),esk5_2(X183,X184),esk4_2(X183,X184))
| X184 = k2_autgroup(X183)
| ~ v1_funct_1(X184)
| ~ v1_funct_2(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| ~ m2_relset_1(X184,k2_zfmisc_1(k1_autgroup(X183),k1_autgroup(X183)),k1_autgroup(X183))
| v3_struct_0(X183)
| ~ v1_group_1(X183)
| ~ v3_group_1(X183)
| ~ v4_group_1(X183)
| ~ l1_group_1(X183) ) ),
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_20])])])])]) ).
cnf(c_0_30,plain,
( m2_fraenkel(X1,X3,X4,X2)
| v1_xboole_0(X4)
| ~ m1_subset_1(X1,X2)
| ~ m1_fraenkel(X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( v3_struct_0(X1)
| m1_fraenkel(k1_autgroup(X1),u1_struct_0(X1),u1_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_22]) ).
cnf(c_0_32,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_33,plain,
! [X281,X282,X283] :
( ( ~ m2_relset_1(X283,X281,X282)
| m1_relset_1(X283,X281,X282) )
& ( ~ m1_relset_1(X283,X281,X282)
| m2_relset_1(X283,X281,X282) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_34,plain,
( ~ v1_xboole_0(X1)
| ~ m1_fraenkel(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v1_group_1(X1)
& v3_group_1(X1)
& v4_group_1(X1)
& l1_group_1(X1) )
=> ( v1_funct_1(k2_autgroup(X1))
& v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
& m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_autgroup]) ).
cnf(c_0_36,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_26]) ).
cnf(c_0_37,negated_conjecture,
m2_fraenkel(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_41,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_42,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_43,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_27]) ).
cnf(c_0_44,plain,
( v1_xboole_0(X1)
| v1_xboole_0(X2)
| k2_binop_1(X1,X2,X4,X3,X5,X6) = k1_binop_1(X3,X5,X6)
| ~ v1_funct_1(X3)
| ~ v1_funct_2(X3,k2_zfmisc_1(X1,X2),X4)
| ~ m1_relset_1(X3,k2_zfmisc_1(X1,X2),X4)
| ~ m1_subset_1(X5,X1)
| ~ m1_subset_1(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_45,plain,
( k2_binop_1(k1_autgroup(X2),k1_autgroup(X2),k1_autgroup(X2),X1,X3,X4) = k7_funct_2(u1_struct_0(X2),u1_struct_0(X2),u1_struct_0(X2),X4,X3)
| v3_struct_0(X2)
| X1 != k2_autgroup(X2)
| ~ m2_fraenkel(X3,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ m2_fraenkel(X4,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_autgroup(X2))
| ~ m2_relset_1(X1,k2_zfmisc_1(k1_autgroup(X2),k1_autgroup(X2)),k1_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_29]) ).
cnf(c_0_46,plain,
( m2_fraenkel(X1,u1_struct_0(X2),u1_struct_0(X2),k1_autgroup(X2))
| v3_struct_0(X2)
| ~ m1_subset_1(X1,k1_autgroup(X2))
| ~ l1_group_1(X2)
| ~ v4_group_1(X2)
| ~ v3_group_1(X2)
| ~ v1_group_1(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_47,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_48,plain,
( v3_struct_0(X1)
| ~ v1_xboole_0(k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
fof(c_0_49,plain,
! [X194] :
( ( v1_funct_1(k2_autgroup(X194))
| v3_struct_0(X194)
| ~ v1_group_1(X194)
| ~ v3_group_1(X194)
| ~ v4_group_1(X194)
| ~ l1_group_1(X194) )
& ( v1_funct_2(k2_autgroup(X194),k2_zfmisc_1(k1_autgroup(X194),k1_autgroup(X194)),k1_autgroup(X194))
| v3_struct_0(X194)
| ~ v1_group_1(X194)
| ~ v3_group_1(X194)
| ~ v4_group_1(X194)
| ~ l1_group_1(X194) )
& ( m2_relset_1(k2_autgroup(X194),k2_zfmisc_1(k1_autgroup(X194),k1_autgroup(X194)),k1_autgroup(X194))
| v3_struct_0(X194)
| ~ v1_group_1(X194)
| ~ v3_group_1(X194)
| ~ v4_group_1(X194)
| ~ l1_group_1(X194) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_50,plain,
( m1_subset_1(X1,X4)
| v1_xboole_0(X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| ~ m1_fraenkel(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_51,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_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_52,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_38])]) ).
cnf(c_0_53,negated_conjecture,
m2_fraenkel(esk2_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_36,c_0_43]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_54,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(X4,X3,X2)
| v3_struct_0(X1)
| X4 != k2_autgroup(X1)
| ~ m2_relset_1(X4,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_2(X4,k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_autgroup(X1))
| ~ v1_funct_1(X4)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
( m2_relset_1(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_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_49]) ).
cnf(c_0_56,plain,
( v1_funct_1(k2_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_49]) ).
cnf(c_0_57,plain,
( v1_funct_2(k2_autgroup(X1),k2_zfmisc_1(k1_autgroup(X1),k1_autgroup(X1)),k1_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_49]) ).
cnf(c_0_58,negated_conjecture,
( m1_subset_1(esk3_0,k1_autgroup(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( m1_subset_1(esk2_0,k1_autgroup(esk1_0))
| ~ m1_fraenkel(k1_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_52]) ).
cnf(c_0_60,negated_conjecture,
k1_binop_1(k2_autgroup(esk1_0),esk2_0,esk3_0) != k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_61,plain,
( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,X3) = k1_binop_1(k2_autgroup(X1),X3,X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,k1_autgroup(X1))
| ~ m1_subset_1(X3,k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
cnf(c_0_62,negated_conjecture,
m1_subset_1(esk3_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_58,c_0_31]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_63,negated_conjecture,
m1_subset_1(esk2_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_59,c_0_31]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_64,negated_conjecture,
$false,
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(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_63]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP624+1 : TPTP v9.2.1. Released v3.4.0.
% 0.12/0.12 % 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
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:47:56 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.85/3.11 % Version : CSE_E---1.7
% 3.85/3.11 % Problem : theBenchmark.p
% 3.85/3.11 % SZS status Theorem for theBenchmark.p
% 3.85/3.11 % SZS output start CNFRefutation
% See solution above
% 3.96/3.12 % Total time : 2.372s
%------------------------------------------------------------------------------