%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:14:58 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 15 unt; 0 def)
% Number of atoms : 270 ( 5 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 330 ( 129 ~; 121 |; 32 &)
% ( 9 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 126 ( 9 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_relset_1_48,conjecture,
! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_48) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(p31,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(p17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( ilf_type(X1,set_type)
& relation_like(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(p29,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X4,X2)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_48]) ).
fof(c_0_11,plain,
! [X25,X26,X27,X28] :
( ( ~ ilf_type(X25,set_type)
| ~ ilf_type(X26,set_type)
| ilf_type(X28,subset_type(cross_product(X25,X26)))
| ~ ilf_type(X28,relation_type(X25,X26)) )
& ( ~ ilf_type(X25,set_type)
| ~ ilf_type(X26,set_type)
| ilf_type(X27,relation_type(X25,X26))
| ~ ilf_type(X27,subset_type(cross_product(X25,X26))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).
fof(c_0_12,plain,
! [X86] : ilf_type(X86,set_type),
inference(variable_rename,[status(thm)],[p31]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X1))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,range(X2,X1,X3))
<=> ? [X5] :
( member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X48] :
( ( ~ ilf_type(X48,set_type)
| ilf_type(X48,binary_relation_type)
| ~ ilf_type(X48,set_type)
| ~ relation_like(X48) )
& ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X48,binary_relation_type)
| ilf_type(X48,set_type) )
& ( ~ ilf_type(X48,set_type)
| ~ ilf_type(X48,binary_relation_type)
| relation_like(X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])]) ).
fof(c_0_15,plain,
! [X71,X72,X73] :
( relation_like(X73)
| ~ ilf_type(X73,subset_type(cross_product(X71,X72)))
| ~ ilf_type(X72,set_type)
| ~ ilf_type(X71,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])])]) ).
cnf(c_0_16,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
! [X91] :
( ( member(esk15_0,range(esk13_0,esk12_0,esk14_0))
| member(ordered_pair(esk16_0,esk15_0),esk14_0) )
& ( member(esk15_0,range(esk13_0,esk12_0,esk14_0))
| ilf_type(esk16_0,member_type(esk13_0)) )
& ( ~ member(ordered_pair(X91,esk15_0),esk14_0)
| ~ ilf_type(X91,member_type(esk13_0))
| ~ member(esk15_0,range(esk13_0,esk12_0,esk14_0)) )
& ilf_type(esk15_0,member_type(esk12_0))
& ilf_type(esk14_0,relation_type(esk13_0,esk12_0))
& ilf_type(esk13_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk12_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
cnf(c_0_19,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ ilf_type(X1,relation_type(X2,X3))
| ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
ilf_type(esk14_0,relation_type(esk13_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X80,X81,X82] :
( range(X80,X81,X82) = range_of(X82)
| ~ ilf_type(X82,relation_type(X80,X81))
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X80,set_type) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])])]) ).
fof(c_0_24,plain,
! [X6,X7,X9] :
( ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| member(X6,range_of(X7))
| ~ member(ordered_pair(X9,X6),X7)
| ~ ilf_type(X9,set_type) )
& ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| ~ member(X6,range_of(X7))
| member(ordered_pair(esk1_2(X6,X7),X6),X7) )
& ( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| ~ member(X6,range_of(X7))
| ilf_type(esk1_2(X6,X7),set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])])]) ).
cnf(c_0_25,plain,
( ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17])]) ).
cnf(c_0_27,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk13_0,esk12_0))),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| range(X1,X2,X3) = range_of(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p10]) ).
fof(c_0_30,plain,
! [X13,X14,X15,X16,X17] :
( ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,relation_type(X13,X14))
| ~ member(ordered_pair(X15,X16),X17)
| member(X16,X14) )
& ( ~ ilf_type(X13,set_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X17,relation_type(X13,X14))
| ~ member(ordered_pair(X15,X16),X17)
| member(X15,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])])]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2))
| member(ordered_pair(esk1_2(X1,X2),X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( ~ relation_like(X1)
| ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
relation_like(esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ ilf_type(X3,relation_type(X1,X2))
| range(X1,X2,X3) = range_of(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17])]) ).
fof(c_0_35,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p8]) ).
fof(c_0_36,plain,
! [X36,X37] :
( ( ~ ilf_type(X36,set_type)
| empty(X36)
| member(esk4_1(X36),X36) )
& ( ~ ilf_type(X36,set_type)
| empty(X36)
| ilf_type(esk4_1(X36),set_type) )
& ( ~ ilf_type(X36,set_type)
| ~ member(X37,X36)
| ~ ilf_type(X37,set_type)
| ~ empty(X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])])]) ).
cnf(c_0_37,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X2,X5))
| ~ member(ordered_pair(X1,X3),X4)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,range_of(X2))
| member(ordered_pair(esk1_2(X1,X2),X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_17])]) ).
cnf(c_0_39,negated_conjecture,
ilf_type(esk14_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( member(esk15_0,range(esk13_0,esk12_0,esk14_0))
| ilf_type(esk16_0,member_type(esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,negated_conjecture,
range(esk13_0,esk12_0,esk14_0) = range_of(esk14_0),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
fof(c_0_42,plain,
! [X32,X33] :
( ( ~ ilf_type(X32,set_type)
| ~ ilf_type(X33,set_type)
| empty(X33)
| ilf_type(X32,member_type(X33))
| ~ member(X32,X33) )
& ( ~ ilf_type(X32,set_type)
| ~ ilf_type(X33,set_type)
| empty(X33)
| member(X32,X33)
| ~ ilf_type(X32,member_type(X33)) ) ),
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_35])])])])]) ).
cnf(c_0_43,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ ilf_type(X4,relation_type(X2,X5))
| ~ member(ordered_pair(X1,X3),X4)
| member(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_45,negated_conjecture,
( ~ member(X1,range_of(esk14_0))
| member(ordered_pair(esk1_2(X1,esk14_0),X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| member(esk15_0,range_of(esk14_0)) ),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2)
| empty(X2)
| ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( ~ member(X2,X1)
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_17]),c_0_17])]) ).
cnf(c_0_49,negated_conjecture,
( ~ member(ordered_pair(X1,X2),esk14_0)
| member(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_50,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| member(ordered_pair(esk1_2(esk15_0,esk14_0),esk15_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(ordered_pair(X1,esk15_0),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0))
| ~ member(esk15_0,range(esk13_0,esk12_0,esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,plain,
( ~ member(X1,X2)
| ilf_type(X1,member_type(X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_17]),c_0_17])]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| member(esk1_2(esk15_0,esk14_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X1,set_type)
| member(X2,range_of(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,negated_conjecture,
( ~ ilf_type(X1,member_type(esk13_0))
| ~ member(esk15_0,range_of(esk14_0))
| ~ member(ordered_pair(X1,esk15_0),esk14_0) ),
inference(rw,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_56,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X3,X1),X2)
| member(X1,range_of(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_17]),c_0_17])]) ).
cnf(c_0_58,negated_conjecture,
( member(esk15_0,range(esk13_0,esk12_0,esk14_0))
| member(ordered_pair(esk16_0,esk15_0),esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_59,negated_conjecture,
ilf_type(esk16_0,member_type(esk13_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_46]),c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( ~ member(ordered_pair(X2,X1),esk14_0)
| member(X1,range_of(esk14_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_39]) ).
cnf(c_0_61,negated_conjecture,
( member(esk15_0,range_of(esk14_0))
| member(ordered_pair(esk16_0,esk15_0),esk14_0) ),
inference(rw,[status(thm)],[c_0_58,c_0_41]) ).
cnf(c_0_62,negated_conjecture,
~ member(ordered_pair(esk16_0,esk15_0),esk14_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_59]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
member(esk15_0,range_of(esk14_0)),
inference(sr,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,negated_conjecture,
member(ordered_pair(esk1_2(esk15_0,esk14_0),esk15_0),esk14_0),
inference(spm,[status(thm)],[c_0_45,c_0_63]) ).
cnf(c_0_65,negated_conjecture,
member(esk1_2(esk15_0,esk14_0),esk13_0),
inference(spm,[status(thm)],[c_0_49,c_0_64]) ).
cnf(c_0_66,negated_conjecture,
( ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(X1,esk15_0),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_63])]) ).
cnf(c_0_67,negated_conjecture,
ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)),
inference(spm,[status(thm)],[c_0_52,c_0_65]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET681+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:37:07 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 Running first-order theorem proving
% 0.16/0.40 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
% 0.16/0.46 % Version: 3.5.1
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.46 % Starting sh5l with 300s (1) cores
% 0.16/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1664429 completed with status 0
% 0.16/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.46 % No SInE strategy applied
% 0.16/0.46 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.16/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.16/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S2g with pid 1664437 completed with status 0
% 0.16/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S2g
% 0.16/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.46 % No SInE strategy applied
% 0.16/0.46 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.16/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2g with 136s (1) cores
% 0.16/0.46 % Preprocessing time : 0.002 s
% 0.16/0.46 % Presaturation interreduction done
% 0.16/0.46
% 0.16/0.46 % Proof found!
% 0.16/0.46 % SZS status Theorem
% 0.16/0.46 % SZS output start CNFRefutation
% See solution above
% 0.16/0.46 % Parsed axioms : 32
% 0.16/0.46 % Removed by relevancy pruning/SinE : 0
% 0.16/0.46 % Initial clauses : 65
% 0.16/0.46 % Removed in clause preprocessing : 3
% 0.16/0.46 % Initial clauses in saturation : 62
% 0.16/0.46 % Processed clauses : 377
% 0.16/0.46 % ...of these trivial : 19
% 0.16/0.46 % ...subsumed : 80
% 0.16/0.46 % ...remaining for further processing : 278
% 0.16/0.46 % Other redundant clauses eliminated : 1
% 0.16/0.46 % Clauses deleted for lack of memory : 0
% 0.16/0.46 % Backward-subsumed : 5
% 0.16/0.46 % Backward-rewritten : 35
% 0.16/0.46 % Generated clauses : 558
% 0.16/0.46 % ...of the previous two non-redundant : 510
% 0.16/0.46 % ...aggressively subsumed : 0
% 0.16/0.46 % Contextual simplify-reflections : 8
% 0.16/0.46 % Paramodulations : 544
% 0.16/0.46 % Factorizations : 2
% 0.16/0.46 % NegExts : 0
% 0.16/0.46 % Equation resolutions : 1
% 0.16/0.46 % Disequality decompositions : 0
% 0.16/0.46 % Total rewrite steps : 219
% 0.16/0.46 % ...of those cached : 140
% 0.16/0.46 % Propositional unsat checks : 0
% 0.16/0.46 % Propositional check models : 0
% 0.16/0.46 % Propositional check unsatisfiable : 0
% 0.16/0.46 % Propositional clauses : 0
% 0.16/0.46 % Propositional clauses after purity: 0
% 0.16/0.46 % Propositional unsat core size : 0
% 0.16/0.46 % Propositional preprocessing time : 0.000
% 0.16/0.46 % Propositional encoding time : 0.000
% 0.16/0.46 % Propositional solver time : 0.000
% 0.16/0.46 % Success case prop preproc time : 0.000
% 0.16/0.46 % Success case prop encoding time : 0.000
% 0.16/0.46 % Success case prop solver time : 0.000
% 0.16/0.46 % Current number of processed clauses : 182
% 0.16/0.46 % Positive orientable unit clauses : 69
% 0.16/0.46 % Positive unorientable unit clauses: 1
% 0.16/0.46 % Negative unit clauses : 8
% 0.16/0.46 % Non-unit-clauses : 104
% 0.16/0.46 % Current number of unprocessed clauses: 239
% 0.16/0.46 % ...number of literals in the above : 513
% 0.16/0.46 % Current number of archived formulas : 0
% 0.16/0.46 % Current number of archived clauses : 95
% 0.16/0.46 % Clause-clause subsumption calls (NU) : 2577
% 0.16/0.46 % Rec. Clause-clause subsumption calls : 2121
% 0.16/0.46 % Non-unit clause-clause subsumptions : 66
% 0.16/0.46 % Unit Clause-clause subsumption calls : 695
% 0.16/0.46 % Rewrite failures with RHS unbound : 0
% 0.16/0.46 % BW rewrite match attempts : 31
% 0.16/0.46 % BW rewrite match successes : 9
% 0.16/0.46 % Condensation attempts : 0
% 0.16/0.46 % Condensation successes : 0
% 0.16/0.46 % Termbank termtop insertions : 13755
% 0.16/0.46 % Search garbage collected termcells : 1436
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.029 s
% 0.16/0.46 % System time : 0.009 s
% 0.16/0.46 % Total time : 0.038 s
% 0.16/0.46 % Maximum resident set size: 3624 pages
% 0.16/0.46
% 0.16/0.46 % -------------------------------------------------
% 0.16/0.46 % User time : 0.121 s
% 0.16/0.46 % System time : 0.036 s
% 0.16/0.46 % Total time : 0.157 s
% 0.16/0.46 % Maximum resident set size: 4608 pages
% 0.16/0.46 % E exiting
%------------------------------------------------------------------------------