%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET810+4 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 23.35s 15.52s
% Output : CNFRefutation 23.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 84 ( 6 avg)
% Number of connectives : 237 ( 65 ~; 106 |; 53 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
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/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV3,conjecture,
! [X1,X2] :
( ( member(X1,on)
& member(X2,on) )
=> ~ ( member(X1,X2)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV3) ).
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/sandbox2/benchmark/Axioms/SET006+4.ax',strict_order) ).
fof(rel_member,axiom,
! [X3,X5] :
( apply(member_predicate,X3,X5)
<=> member(X3,X5) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET006+4.ax',strict_well_order) ).
fof(c_0_6,plain,
! [X67,X68,X69,X70,X71] :
( ( ~ subset(X67,X68)
| ~ member(X69,X67)
| member(X69,X68) )
& ( member(esk1_2(X70,X71),X70)
| subset(X70,X71) )
& ( ~ member(esk1_2(X70,X71),X71)
| subset(X70,X71) ) ),
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)],[subset])])])])])]) ).
fof(c_0_7,plain,
! [X104,X105,X106] :
( ( set(X104)
| ~ member(X104,on) )
& ( strict_well_order(member_predicate,X104)
| ~ member(X104,on) )
& ( ~ member(X105,X104)
| subset(X105,X104)
| ~ member(X104,on) )
& ( member(esk4_1(X106),X106)
| ~ set(X106)
| ~ strict_well_order(member_predicate,X106)
| member(X106,on) )
& ( ~ subset(esk4_1(X106),X106)
| ~ set(X106)
| ~ strict_well_order(member_predicate,X106)
| member(X106,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_8,negated_conjecture,
~ ! [X1,X2] :
( ( member(X1,on)
& member(X2,on) )
=> ~ ( member(X1,X2)
& member(X2,X1) ) ),
inference(assume_negation,[status(cth)],[thV3]) ).
cnf(c_0_9,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| ~ member(X1,X2)
| ~ member(X2,on) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( member(esk14_0,on)
& member(esk15_0,on)
& member(esk14_0,esk15_0)
& member(esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X2,on)
| ~ member(X1,X3)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X128,X129,X130,X131,X132,X133,X134,X135,X136] :
( ( ~ member(X130,X129)
| ~ member(X131,X129)
| ~ apply(X128,X130,X131)
| ~ apply(X128,X131,X130)
| ~ strict_order(X128,X129) )
& ( ~ member(X132,X129)
| ~ member(X133,X129)
| ~ member(X134,X129)
| ~ apply(X128,X132,X133)
| ~ apply(X128,X133,X134)
| apply(X128,X132,X134)
| ~ strict_order(X128,X129) )
& ( member(esk11_2(X135,X136),X136)
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk12_2(X135,X136),X136)
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk13_2(X135,X136),X136)
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( apply(X135,esk11_2(X135,X136),esk12_2(X135,X136))
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( apply(X135,esk12_2(X135,X136),esk13_2(X135,X136))
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( ~ apply(X135,esk11_2(X135,X136),esk13_2(X135,X136))
| member(esk9_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk11_2(X135,X136),X136)
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk12_2(X135,X136),X136)
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk13_2(X135,X136),X136)
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( apply(X135,esk11_2(X135,X136),esk12_2(X135,X136))
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( apply(X135,esk12_2(X135,X136),esk13_2(X135,X136))
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( ~ apply(X135,esk11_2(X135,X136),esk13_2(X135,X136))
| member(esk10_2(X135,X136),X136)
| strict_order(X135,X136) )
& ( member(esk11_2(X135,X136),X136)
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( member(esk12_2(X135,X136),X136)
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( member(esk13_2(X135,X136),X136)
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( apply(X135,esk11_2(X135,X136),esk12_2(X135,X136))
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( apply(X135,esk12_2(X135,X136),esk13_2(X135,X136))
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( ~ apply(X135,esk11_2(X135,X136),esk13_2(X135,X136))
| apply(X135,esk9_2(X135,X136),esk10_2(X135,X136))
| strict_order(X135,X136) )
& ( member(esk11_2(X135,X136),X136)
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) )
& ( member(esk12_2(X135,X136),X136)
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) )
& ( member(esk13_2(X135,X136),X136)
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) )
& ( apply(X135,esk11_2(X135,X136),esk12_2(X135,X136))
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) )
& ( apply(X135,esk12_2(X135,X136),esk13_2(X135,X136))
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) )
& ( ~ apply(X135,esk11_2(X135,X136),esk13_2(X135,X136))
| apply(X135,esk10_2(X135,X136),esk9_2(X135,X136))
| strict_order(X135,X136) ) ),
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_15,plain,
! [X126,X127] :
( ( ~ apply(member_predicate,X126,X127)
| member(X126,X127) )
& ( ~ member(X126,X127)
| apply(member_predicate,X126,X127) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rel_member])]) ).
fof(c_0_16,plain,
! [X108,X109,X110,X111,X113,X114,X117] :
( ( strict_order(X108,X109)
| ~ strict_well_order(X108,X109) )
& ( ~ subset(X110,X109)
| ~ member(X111,X110)
| least(esk5_3(X108,X109,X110),X108,X110)
| ~ strict_well_order(X108,X109) )
& ( subset(esk6_2(X113,X114),X114)
| ~ strict_order(X113,X114)
| strict_well_order(X113,X114) )
& ( member(esk7_2(X113,X114),esk6_2(X113,X114))
| ~ strict_order(X113,X114)
| strict_well_order(X113,X114) )
& ( ~ least(X117,X113,esk6_2(X113,X114))
| ~ strict_order(X113,X114)
| strict_well_order(X113,X114) ) ),
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])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X2,esk14_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
member(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,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_14]) ).
cnf(c_0_20,plain,
( apply(member_predicate,X1,X2)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( strict_order(X1,X2)
| ~ strict_well_order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( strict_well_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
member(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,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_19,c_0_20]) ).
cnf(c_0_26,plain,
( strict_order(member_predicate,X1)
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
member(esk14_0,esk14_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_25,c_0_26,c_0_20,c_0_27,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET810+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:36:28 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 23.35/15.52 % Version : CSE_E---1.7
% 23.35/15.52 % Problem : theBenchmark.p
% 23.35/15.52 % SZS status Theorem for theBenchmark.p
% 23.35/15.52 % SZS output start CNFRefutation
% See solution above
% 23.45/15.60 % Total time : 12.393s
%------------------------------------------------------------------------------