%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP632+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:40:28 PM UTC 2026
% Result : Theorem 108.69s 18.61s
% Output : CNFRefutation 108.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 25 unt; 0 def)
% Number of atoms : 265 ( 33 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 287 ( 103 ~; 91 |; 68 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-5 aty)
% Number of variables : 127 ( 3 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',fc1_struct_0) ).
fof(t30_autgroup,conjecture,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,k6_autgroup(X1,k2_group_1(X1))) = X2
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_autgroup) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+212.ax',dt_l1_group_1) ).
fof(dt_m2_fraenkel,axiom,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( m2_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+34.ax',dt_m2_fraenkel) ).
fof(t24_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_autgroup) ).
fof(dt_k4_autgroup,axiom,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(redefinition_k6_partfun1,axiom,
! [X1] : k6_partfun1(X1) = k6_relat_1(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+17.ax',redefinition_k6_partfun1) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
<=> r1_tarski(X3,k2_zfmisc_1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+16.ax',d1_relset_1) ).
fof(t28_relset_1,axiom,
! [X1] : r1_tarski(k6_relat_1(X1),k2_zfmisc_1(X1,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+16.ax',t28_relset_1) ).
fof(dt_k6_partfun1,axiom,
! [X1] :
( m2_relset_1(k6_partfun1(X1),X1,X1)
& v1_partfun1(k6_partfun1(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+17.ax',dt_k6_partfun1) ).
fof(redefinition_k7_funct_2,axiom,
! [X1,X2,X3,X4,X5] :
( ( m1_relset_1(X5,X2,X3)
& v1_funct_2(X5,X2,X3)
& v1_funct_1(X5)
& m1_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+20.ax',redefinition_k7_funct_2) ).
fof(t36_partfun1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k5_relat_1(k6_relat_1(X1),X3) = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+17.ax',t36_partfun1) ).
fof(cc1_funct_2,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> ( ( v1_partfun1(X3,X1,X2)
& v1_funct_1(X3) )
=> ( v1_funct_2(X3,X1,X2)
& v1_funct_1(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+20.ax',cc1_funct_2) ).
fof(fc2_funct_1,axiom,
! [X1] :
( v1_funct_1(k6_relat_1(X1))
& v1_relat_1(k6_relat_1(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+11.ax',fc2_funct_1) ).
fof(t37_partfun1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k5_relat_1(X3,k6_relat_1(X2)) = X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+17.ax',t37_partfun1) ).
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/Axioms/SET007/SET007+16.ax',redefinition_m2_relset_1) ).
fof(c_0_16,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,k6_autgroup(X1,k2_group_1(X1))) = X2
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),X2) = X2 ) ) ),
inference(assume_negation,[status(cth)],[t30_autgroup]) ).
fof(c_0_18,plain,
! [X5038] :
( ~ v1_xboole_0(u1_struct_0(X5038))
| ~ l1_struct_0(X5038)
| v3_struct_0(X5038) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X5047] :
( l1_struct_0(X5047)
| ~ l1_group_1(X5047) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m2_fraenkel(X2,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1))
=> ( k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),X2,k6_autgroup(X1,k2_group_1(X1))) = X2
& k7_funct_2(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X1),k6_autgroup(X1,k2_group_1(X1)),X2) = X2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X1,X2,X3] :
( ( m1_fraenkel(X3,X1,X2)
& ~ v1_xboole_0(X2) )
=> ! [X4] :
( m2_fraenkel(X4,X1,X2,X3)
=> ( m2_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4) ) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_fraenkel]) ).
cnf(c_0_22,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( ~ l1_group_1(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,negated_conjecture,
( ( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0,k6_autgroup(esk1_0,k2_group_1(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,k2_group_1(esk1_0)),esk2_0) != esk2_0 )
& m2_fraenkel(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0),k4_autgroup(esk1_0))
& l1_group_1(esk1_0)
& v4_group_1(esk1_0)
& v3_group_1(esk1_0)
& v1_group_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_25,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[t24_autgroup]) ).
fof(c_0_26,plain,
! [X1638,X1639,X1640,X1641] :
( ( ~ m1_fraenkel(X1640,X1638,X1639)
| v1_xboole_0(X1639)
| ~ m2_fraenkel(X1641,X1638,X1639,X1640)
| m2_relset_1(X1641,X1638,X1639) )
& ( ~ m1_fraenkel(X1640,X1638,X1639)
| v1_xboole_0(X1639)
| ~ m2_fraenkel(X1641,X1638,X1639,X1640)
| v1_funct_2(X1641,X1638,X1639) )
& ( ~ m1_fraenkel(X1640,X1638,X1639)
| v1_xboole_0(X1639)
| ~ m2_fraenkel(X1641,X1638,X1639,X1640)
| v1_funct_1(X1641) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
cnf(c_0_27,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_group_1(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
l1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X1] :
( ( l1_group_1(X1)
& v4_group_1(X1)
& v3_group_1(X1)
& v1_group_1(X1)
& ~ v3_struct_0(X1) )
=> m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k4_autgroup]) ).
fof(c_0_31,plain,
! [X92] :
( k6_autgroup(X92,k2_group_1(X92)) = k6_partfun1(u1_struct_0(X92))
| ~ l1_group_1(X92)
| ~ v4_group_1(X92)
| ~ v3_group_1(X92)
| ~ v1_group_1(X92)
| v3_struct_0(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_32,plain,
! [X681] : k6_partfun1(X681) = k6_relat_1(X681),
inference(variable_rename,[status(thm)],[redefinition_k6_partfun1]) ).
cnf(c_0_33,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,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_24]) ).
cnf(c_0_35,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
fof(c_0_36,plain,
! [X156] :
( m1_fraenkel(k4_autgroup(X156),u1_struct_0(X156),u1_struct_0(X156))
| ~ l1_group_1(X156)
| ~ v4_group_1(X156)
| ~ v3_group_1(X156)
| ~ v1_group_1(X156)
| v3_struct_0(X156) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_37,plain,
! [X188,X189,X190] :
( ( m1_relset_1(X190,X188,X189)
| ~ r1_tarski(X190,k2_zfmisc_1(X188,X189)) )
& ( r1_tarski(X190,k2_zfmisc_1(X188,X189))
| ~ m1_relset_1(X190,X188,X189) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])])]) ).
fof(c_0_38,plain,
! [X4138] : r1_tarski(k6_relat_1(X4138),k2_zfmisc_1(X4138,X4138)),
inference(variable_rename,[status(thm)],[t28_relset_1]) ).
fof(c_0_39,plain,
! [X680] :
( m2_relset_1(k6_partfun1(X680),X680,X680)
& v1_partfun1(k6_partfun1(X680),X680,X680) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
cnf(c_0_40,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| k6_autgroup(X1,k2_group_1(X1)) = k6_partfun1(u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
k6_partfun1(X1) = k6_relat_1(X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,plain,
! [X1,X2,X3,X4,X5] :
( ( m1_relset_1(X5,X2,X3)
& v1_funct_2(X5,X2,X3)
& v1_funct_1(X5)
& m1_relset_1(X4,X1,X2)
& v1_funct_2(X4,X1,X2)
& v1_funct_1(X4)
& ~ v1_xboole_0(X2) )
=> k7_funct_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_funct_2]) ).
fof(c_0_43,plain,
! [X4143,X4144,X4145] :
( k5_relat_1(k6_relat_1(X4143),X4145) = X4145
| ~ m2_relset_1(X4145,X4143,X4144) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t36_partfun1])])]) ).
cnf(c_0_44,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| m2_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_45,plain,
( ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| m1_fraenkel(k4_autgroup(X1),u1_struct_0(X1),u1_struct_0(X1))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_47,negated_conjecture,
v3_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_48,negated_conjecture,
v1_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_49,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| v1_funct_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_50,plain,
! [X3277,X3278,X3279] :
( ( ~ m1_relset_1(X3279,X3277,X3278)
| ~ v1_partfun1(X3279,X3277,X3278)
| ~ v1_funct_1(X3279)
| v1_funct_2(X3279,X3277,X3278) )
& ( ~ m1_relset_1(X3279,X3277,X3278)
| ~ v1_partfun1(X3279,X3277,X3278)
| ~ v1_funct_1(X3279)
| v1_funct_1(X3279) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])])]) ).
cnf(c_0_51,plain,
( ~ r1_tarski(X1,k2_zfmisc_1(X2,X3))
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_52,plain,
r1_tarski(k6_relat_1(X1),k2_zfmisc_1(X1,X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,plain,
v1_partfun1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_54,plain,
! [X4108] :
( v1_funct_1(k6_relat_1(X4108))
& v1_relat_1(k6_relat_1(X4108)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_55,plain,
( ~ m1_fraenkel(X4,X2,X3)
| ~ m2_fraenkel(X1,X2,X3,X4)
| v1_xboole_0(X3)
| v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_56,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0,k6_autgroup(esk1_0,k2_group_1(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,k2_group_1(esk1_0)),esk2_0) != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_57,plain,
( ~ l1_group_1(X1)
| ~ v1_group_1(X1)
| ~ v3_group_1(X1)
| ~ v4_group_1(X1)
| v3_struct_0(X1)
| k6_autgroup(X1,k2_group_1(X1)) = k6_relat_1(u1_struct_0(X1)) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_58,plain,
! [X59,X60,X61,X62,X63] :
( k7_funct_2(X59,X60,X61,X62,X63) = k5_relat_1(X62,X63)
| ~ m1_relset_1(X63,X60,X61)
| ~ v1_funct_2(X63,X60,X61)
| ~ v1_funct_1(X63)
| ~ m1_relset_1(X62,X59,X60)
| ~ v1_funct_2(X62,X59,X60)
| ~ v1_funct_1(X62)
| v1_xboole_0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])]) ).
cnf(c_0_59,plain,
( ~ m2_relset_1(X1,X2,X3)
| k5_relat_1(k6_relat_1(X2),X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_60,negated_conjecture,
m2_relset_1(esk2_0,u1_struct_0(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_44,c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_28])]),c_0_29]) ).
cnf(c_0_61,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_funct_2(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_35]) ).
cnf(c_0_62,plain,
( ~ m1_relset_1(X1,X2,X3)
| ~ v1_partfun1(X1,X2,X3)
| ~ v1_funct_1(X1)
| v1_funct_2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,plain,
m1_relset_1(k6_relat_1(X1),X1,X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_64,plain,
v1_partfun1(k6_relat_1(X1),X1,X1),
inference(rw,[status(thm)],[c_0_53,c_0_41]) ).
cnf(c_0_65,plain,
v1_funct_1(k6_relat_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,negated_conjecture,
( ~ m1_fraenkel(k4_autgroup(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| v1_funct_1(esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_34]),c_0_35]) ).
fof(c_0_67,plain,
! [X4146,X4147,X4148] :
( k5_relat_1(X4148,k6_relat_1(X4147)) = X4148
| ~ m2_relset_1(X4148,X4146,X4147) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_partfun1])])]) ).
cnf(c_0_68,negated_conjecture,
( k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),k6_relat_1(u1_struct_0(esk1_0)),esk2_0) != esk2_0
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0,k6_relat_1(u1_struct_0(esk1_0))) != esk2_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_56,c_0_57]),c_0_46]),c_0_47]),c_0_48]),c_0_28])]),c_0_29]) ).
cnf(c_0_69,plain,
( ~ m1_relset_1(X4,X1,X5)
| ~ v1_funct_2(X4,X1,X5)
| ~ v1_funct_1(X4)
| ~ m1_relset_1(X2,X3,X1)
| ~ v1_funct_2(X2,X3,X1)
| ~ v1_funct_1(X2)
| k7_funct_2(X3,X1,X5,X2,X4) = k5_relat_1(X2,X4)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,negated_conjecture,
k5_relat_1(k6_relat_1(u1_struct_0(esk1_0)),esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
v1_funct_2(esk2_0,u1_struct_0(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_61,c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_28])]),c_0_29]) ).
cnf(c_0_72,plain,
v1_funct_2(k6_relat_1(X1),X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_73,negated_conjecture,
v1_funct_1(esk2_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_66,c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_28])]),c_0_29]) ).
cnf(c_0_74,plain,
( ~ m2_relset_1(X1,X2,X3)
| k5_relat_1(X1,k6_relat_1(X3)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( ~ m1_relset_1(esk2_0,u1_struct_0(esk1_0),u1_struct_0(esk1_0))
| k7_funct_2(u1_struct_0(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0),esk2_0,k6_relat_1(u1_struct_0(esk1_0))) != esk2_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71]),c_0_72]),c_0_63]),c_0_73]),c_0_65])]),c_0_35]) ).
cnf(c_0_76,negated_conjecture,
k5_relat_1(esk2_0,k6_relat_1(u1_struct_0(esk1_0))) = esk2_0,
inference(spm,[status(thm)],[c_0_74,c_0_60]) ).
fof(c_0_77,plain,
! [X194,X195,X196] :
( ( m2_relset_1(X196,X194,X195)
| ~ m1_relset_1(X196,X194,X195) )
& ( m1_relset_1(X196,X194,X195)
| ~ m2_relset_1(X196,X194,X195) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
cnf(c_0_78,negated_conjecture,
~ m1_relset_1(esk2_0,u1_struct_0(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_69]),c_0_76]),c_0_72]),c_0_71]),c_0_63]),c_0_65]),c_0_73])]),c_0_35]) ).
cnf(c_0_79,plain,
( ~ m2_relset_1(X1,X2,X3)
| m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_80,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_60])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP632+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n014.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 20:22:09 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.69/18.61 % Version: 3.5.1
% 108.69/18.61 % Preprocessing class: FMLLMLLLSSSNFFN.
% 108.69/18.61 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 108.69/18.61 % Starting new_bool_3 with 897s (3) cores
% 108.69/18.61 % Starting new_bool_1 with 897s (3) cores
% 108.69/18.61 % Starting sh5l with 299s (1) cores
% 108.69/18.61 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 299s (1) cores
% 108.69/18.61 % new_bool_3 with pid 2280691 completed with status 0
% 108.69/18.61 % Result found by new_bool_3
% 108.69/18.61 % Preprocessing class: FMLLMLLLSSSNFFN.
% 108.69/18.61 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 108.69/18.61 % Starting new_bool_3 with 897s (3) cores
% 108.69/18.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 108.69/18.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 108.69/18.61 % Search class: FGHSM-SMLM32-MFFFFFNN
% 108.69/18.61 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 108.69/18.61 % Starting SubtermCWHack with 81s (1) cores
% 108.69/18.61 % Starting new_bool_3 with 90s (1) cores
% 108.69/18.61 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 108.69/18.61 % C12_02_nc_SAT001_MinMin_p005000_rr with pid 2280701 completed with status 0
% 108.69/18.61 % Result found by C12_02_nc_SAT001_MinMin_p005000_rr
% 108.69/18.61 % Preprocessing class: FMLLMLLLSSSNFFN.
% 108.69/18.61 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 108.69/18.61 % Starting new_bool_3 with 897s (3) cores
% 108.69/18.61 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 108.69/18.61 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 108.69/18.61 % Search class: FGHSM-SMLM32-MFFFFFNN
% 108.69/18.61 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 108.69/18.61 % Starting SubtermCWHack with 81s (1) cores
% 108.69/18.61 % Starting new_bool_3 with 90s (1) cores
% 108.69/18.61 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 108.69/18.61 % Preprocessing time : 0.230 s
% 108.69/18.61 % Presaturation interreduction done
% 108.69/18.61
% 108.69/18.61 % Proof found!
% 108.69/18.61 % SZS status Theorem
% 108.69/18.61 % SZS output start CNFRefutation
% See solution above
% 108.69/18.62 % Parsed axioms : 33429
% 108.69/18.62 % Removed by relevancy pruning/SinE : 31229
% 108.69/18.62 % Initial clauses : 5070
% 108.69/18.62 % Removed in clause preprocessing : 165
% 108.69/18.62 % Initial clauses in saturation : 4905
% 108.69/18.62 % Processed clauses : 38294
% 108.69/18.62 % ...of these trivial : 236
% 108.69/18.62 % ...subsumed : 24653
% 108.69/18.62 % ...remaining for further processing : 13405
% 108.69/18.62 % Other redundant clauses eliminated : 1684
% 108.69/18.62 % Clauses deleted for lack of memory : 0
% 108.69/18.62 % Backward-subsumed : 279
% 108.69/18.62 % Backward-rewritten : 138
% 108.69/18.62 % Generated clauses : 180715
% 108.69/18.62 % ...of the previous two non-redundant : 167287
% 108.69/18.62 % ...aggressively subsumed : 0
% 108.69/18.62 % Contextual simplify-reflections : 375
% 108.69/18.62 % Paramodulations : 178999
% 108.69/18.62 % Factorizations : 12
% 108.69/18.62 % NegExts : 0
% 108.69/18.62 % Equation resolutions : 1735
% 108.69/18.62 % Disequality decompositions : 0
% 108.69/18.62 % Total rewrite steps : 40439
% 108.69/18.62 % ...of those cached : 36518
% 108.69/18.62 % Propositional unsat checks : 3
% 108.69/18.62 % Propositional check models : 2
% 108.69/18.62 % Propositional check unsatisfiable : 0
% 108.69/18.62 % Propositional clauses : 0
% 108.69/18.62 % Propositional clauses after purity: 0
% 108.69/18.62 % Propositional unsat core size : 0
% 108.69/18.62 % Propositional preprocessing time : 0.000
% 108.69/18.62 % Propositional encoding time : 0.162
% 108.69/18.62 % Propositional solver time : 0.134
% 108.69/18.62 % Success case prop preproc time : 0.000
% 108.69/18.62 % Success case prop encoding time : 0.000
% 108.69/18.62 % Success case prop solver time : 0.000
% 108.69/18.62 % Current number of processed clauses : 7987
% 108.69/18.62 % Positive orientable unit clauses : 1096
% 108.69/18.62 % Positive unorientable unit clauses: 3
% 108.69/18.62 % Negative unit clauses : 1468
% 108.69/18.62 % Non-unit-clauses : 5420
% 108.69/18.62 % Current number of unprocessed clauses: 137934
% 108.69/18.62 % ...number of literals in the above : 676830
% 108.69/18.62 % Current number of archived formulas : 0
% 108.69/18.62 % Current number of archived clauses : 5002
% 108.69/18.62 % Clause-clause subsumption calls (NU) : 18727156
% 108.69/18.62 % Rec. Clause-clause subsumption calls : 2323671
% 108.69/18.62 % Non-unit clause-clause subsumptions : 11303
% 108.69/18.62 % Unit Clause-clause subsumption calls : 815490
% 108.69/18.62 % Rewrite failures with RHS unbound : 0
% 108.69/18.62 % BW rewrite match attempts : 2481
% 108.69/18.62 % BW rewrite match successes : 349
% 108.69/18.62 % Condensation attempts : 0
% 108.69/18.62 % Condensation successes : 0
% 108.69/18.62 % Termbank termtop insertions : 4286575
% 108.69/18.62 % Search garbage collected termcells : 407852
% 108.69/18.62
% 108.69/18.62 % -------------------------------------------------
% 108.69/18.62 % User time : 15.433 s
% 108.69/18.62 % System time : 0.401 s
% 108.69/18.62 % Total time : 15.833 s
% 108.69/18.62 % Maximum resident set size: 71328 pages
% 108.69/18.62
% 108.69/18.62 % -------------------------------------------------
% 108.69/18.62 % User time : 45.537 s
% 108.69/18.62 % System time : 1.177 s
% 108.69/18.62 % Total time : 46.714 s
% 108.69/18.62 % Maximum resident set size: 54528 pages
% 108.69/18.62 % E exiting
%------------------------------------------------------------------------------