%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET809+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n001.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 05:08:32 PM UTC 2026
% Result : Theorem 13.70s 8.44s
% Output : CNFRefutation 13.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 3 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 84 ( 8 avg)
% Number of connectives : 200 ( 52 ~; 92 |; 45 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(strict_order,axiom,
! [X6,X4] :
( strict_order(X6,X4)
<=> ( ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ~ ( apply(X6,X3,X5)
& apply(X6,X5,X3) ) )
& ! [X3,X5,X8] :
( ( member(X3,X4)
& member(X5,X4)
& member(X8,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X8) )
=> apply(X6,X3,X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',strict_order) ).
fof(rel_member,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',rel_member) ).
fof(strict_well_order,axiom,
! [X6,X4] :
( strict_well_order(X6,X4)
<=> ( strict_order(X6,X4)
& ! [X1] :
( ( subset(X1,X4)
& ? [X3] : member(X3,X1) )
=> ? [X5] : least(X5,X6,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
fof(ordinal_number,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV2,conjecture,
! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV2) ).
fof(c_0_5,plain,
! [X127,X128,X129,X130,X131,X132,X133,X134,X135] :
( ( ~ member(X129,X128)
| ~ member(X130,X128)
| ~ apply(X127,X129,X130)
| ~ apply(X127,X130,X129)
| ~ strict_order(X127,X128) )
& ( ~ member(X131,X128)
| ~ member(X132,X128)
| ~ member(X133,X128)
| ~ apply(X127,X131,X132)
| ~ apply(X127,X132,X133)
| apply(X127,X131,X133)
| ~ strict_order(X127,X128) )
& ( member(esk11_2(X134,X135),X135)
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk12_2(X134,X135),X135)
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk13_2(X134,X135),X135)
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( apply(X134,esk11_2(X134,X135),esk12_2(X134,X135))
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( apply(X134,esk12_2(X134,X135),esk13_2(X134,X135))
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( ~ apply(X134,esk11_2(X134,X135),esk13_2(X134,X135))
| member(esk9_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk11_2(X134,X135),X135)
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk12_2(X134,X135),X135)
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk13_2(X134,X135),X135)
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( apply(X134,esk11_2(X134,X135),esk12_2(X134,X135))
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( apply(X134,esk12_2(X134,X135),esk13_2(X134,X135))
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( ~ apply(X134,esk11_2(X134,X135),esk13_2(X134,X135))
| member(esk10_2(X134,X135),X135)
| strict_order(X134,X135) )
& ( member(esk11_2(X134,X135),X135)
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( member(esk12_2(X134,X135),X135)
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( member(esk13_2(X134,X135),X135)
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( apply(X134,esk11_2(X134,X135),esk12_2(X134,X135))
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( apply(X134,esk12_2(X134,X135),esk13_2(X134,X135))
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( ~ apply(X134,esk11_2(X134,X135),esk13_2(X134,X135))
| apply(X134,esk9_2(X134,X135),esk10_2(X134,X135))
| strict_order(X134,X135) )
& ( member(esk11_2(X134,X135),X135)
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) )
& ( member(esk12_2(X134,X135),X135)
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) )
& ( member(esk13_2(X134,X135),X135)
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) )
& ( apply(X134,esk11_2(X134,X135),esk12_2(X134,X135))
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) )
& ( apply(X134,esk12_2(X134,X135),esk13_2(X134,X135))
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) )
& ( ~ apply(X134,esk11_2(X134,X135),esk13_2(X134,X135))
| apply(X134,esk10_2(X134,X135),esk9_2(X134,X135))
| strict_order(X134,X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[strict_order])])])])])]) ).
fof(c_0_6,plain,
! [X125,X126] :
( ( ~ apply(member_predicate,X125,X126)
| member(X125,X126) )
& ( ~ member(X125,X126)
| apply(member_predicate,X125,X126) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])]) ).
fof(c_0_7,plain,
! [X107,X108,X109,X110,X112,X113,X116] :
( ( strict_order(X107,X108)
| ~ strict_well_order(X107,X108) )
& ( ~ subset(X109,X108)
| ~ member(X110,X109)
| least(esk5_3(X107,X108,X109),X107,X109)
| ~ strict_well_order(X107,X108) )
& ( subset(esk6_2(X112,X113),X113)
| ~ strict_order(X112,X113)
| strict_well_order(X112,X113) )
& ( member(esk7_2(X112,X113),esk6_2(X112,X113))
| ~ strict_order(X112,X113)
| strict_well_order(X112,X113) )
& ( ~ least(X116,X112,esk6_2(X112,X113))
| ~ strict_order(X112,X113)
| strict_well_order(X112,X113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[strict_well_order])])])])])]) ).
fof(c_0_8,plain,
! [X103,X104,X105] :
( ( set(X103)
| ~ member(X103,on) )
& ( strict_well_order(member_predicate,X103)
| ~ member(X103,on) )
& ( ~ member(X104,X103)
| subset(X104,X103)
| ~ member(X103,on) )
& ( member(esk4_1(X105),X105)
| ~ set(X105)
| ~ strict_well_order(member_predicate,X105)
| member(X105,on) )
& ( ~ subset(esk4_1(X105),X105)
| ~ set(X105)
| ~ strict_well_order(member_predicate,X105)
| member(X105,on) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ordinal_number])])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> ~ member(X1,X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thV2])]) ).
cnf(c_0_10,plain,
( ~ member(X1,X2)
| ~ member(X3,X2)
| ~ apply(X4,X1,X3)
| ~ apply(X4,X3,X1)
| ~ strict_order(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( apply(member_predicate,X1,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( strict_order(X1,X2)
| ~ strict_well_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( strict_well_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,negated_conjecture,
( member(esk14_0,on)
& member(esk14_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( ~ apply(member_predicate,X1,X2)
| ~ strict_order(member_predicate,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( strict_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
member(esk14_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_15,c_0_11,c_0_16,c_0_17,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET809+4 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n001.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
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:51:33 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 13.70/8.44 % Version : CSE_E---1.7
% 13.70/8.44 % Problem : theBenchmark.p
% 13.70/8.44 % SZS status Theorem for theBenchmark.p
% 13.70/8.44 % SZS output start CNFRefutation
% See solution above
% 13.70/8.49 % Total time : 6.383s
%------------------------------------------------------------------------------