%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET814+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 : n028.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 1.62s 1.83s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 3 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 84 ( 32 ~; 33 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thV14,conjecture,
! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV14) ).
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(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(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
inference(assume_negation,[status(cth)],[thV14]) ).
fof(c_0_5,plain,
! [X107,X108,X109] :
( ( set(X107)
| ~ member(X107,on) )
& ( strict_well_order(member_predicate,X107)
| ~ member(X107,on) )
& ( ~ member(X108,X107)
| subset(X108,X107)
| ~ member(X107,on) )
& ( member(esk4_1(X109),X109)
| ~ set(X109)
| ~ strict_well_order(member_predicate,X109)
| member(X109,on) )
& ( ~ subset(esk4_1(X109),X109)
| ~ set(X109)
| ~ strict_well_order(member_predicate,X109)
| member(X109,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_6,negated_conjecture,
( member(esk14_0,on)
& ~ subset(sum(esk14_0),esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X70,X71,X72,X73,X74] :
( ( ~ subset(X70,X71)
| ~ member(X72,X70)
| member(X72,X71) )
& ( member(esk1_2(X73,X74),X73)
| subset(X73,X74) )
& ( ~ member(esk1_2(X73,X74),X74)
| subset(X73,X74) ) ),
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])])])])])]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| ~ member(X1,X2)
| ~ member(X2,on) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( subset(X1,esk14_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_12,plain,
! [X95,X96,X98,X99,X100] :
( ( member(esk2_2(X95,X96),X96)
| ~ member(X95,sum(X96)) )
& ( member(X95,esk2_2(X95,X96))
| ~ member(X95,sum(X96)) )
& ( ~ member(X100,X99)
| ~ member(X98,X100)
| member(X98,sum(X99)) ) ),
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)],[sum])])])])])]) ).
cnf(c_0_13,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X2,esk14_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X1,esk2_2(X2,esk14_0))
| ~ member(X2,sum(esk14_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X1,sum(esk14_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(sum(esk14_0),X1),esk14_0)
| subset(sum(esk14_0),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ subset(sum(esk14_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET814+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.32 % Computer : n028.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:37:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.62/1.83 % Version : CSE_E---1.7
% 1.62/1.83 % Problem : theBenchmark.p
% 1.62/1.83 % SZS status Theorem for theBenchmark.p
% 1.62/1.83 % SZS output start CNFRefutation
% See solution above
% 1.62/1.83 % Total time : 1.369s
%------------------------------------------------------------------------------