%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET776+4 : TPTP v9.2.1. Released v2.2.0.
% 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 05:08:28 PM UTC 2026
% Result : Theorem 1.67s 1.84s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 46 ( 6 avg)
% Number of connectives : 188 ( 59 ~; 71 |; 44 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII12,conjecture,
! [X4,X8,X7] :
( ( pre_order(X8,X4)
& ! [X1,X2] :
( ( member(X1,X4)
& member(X2,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X1,X2)
& apply(X8,X2,X1) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X4)
& member(X10,X4)
& member(X11,X4)
& member(X12,X4) )
=> ( ( apply(X7,X9,X11)
& apply(X7,X10,X12)
& apply(X8,X9,X10) )
=> apply(X8,X11,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
fof(pre_order,axiom,
! [X7,X4] :
( pre_order(X7,X4)
<=> ( ! [X3] :
( member(X3,X4)
=> apply(X7,X3,X3) )
& ! [X3,X5,X6] :
( ( member(X3,X4)
& member(X5,X4)
& member(X6,X4) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(c_0_2,negated_conjecture,
~ ! [X4,X8,X7] :
( ( pre_order(X8,X4)
& ! [X1,X2] :
( ( member(X1,X4)
& member(X2,X4) )
=> ( apply(X7,X1,X2)
<=> ( apply(X8,X1,X2)
& apply(X8,X2,X1) ) ) ) )
=> ! [X9,X10,X11,X12] :
( ( member(X9,X4)
& member(X10,X4)
& member(X11,X4)
& member(X12,X4) )
=> ( ( apply(X7,X9,X11)
& apply(X7,X10,X12)
& apply(X8,X9,X10) )
=> apply(X8,X11,X12) ) ) ),
inference(assume_negation,[status(cth)],[thIII12]) ).
fof(c_0_3,plain,
! [X144,X145,X146,X147,X148,X149,X150,X151] :
( ( ~ member(X146,X145)
| apply(X144,X146,X146)
| ~ pre_order(X144,X145) )
& ( ~ member(X147,X145)
| ~ member(X148,X145)
| ~ member(X149,X145)
| ~ apply(X144,X147,X148)
| ~ apply(X144,X148,X149)
| apply(X144,X147,X149)
| ~ pre_order(X144,X145) )
& ( member(esk12_2(X150,X151),X151)
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( member(esk13_2(X150,X151),X151)
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( member(esk14_2(X150,X151),X151)
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( apply(X150,esk12_2(X150,X151),esk13_2(X150,X151))
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( apply(X150,esk13_2(X150,X151),esk14_2(X150,X151))
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( ~ apply(X150,esk12_2(X150,X151),esk14_2(X150,X151))
| member(esk11_2(X150,X151),X151)
| pre_order(X150,X151) )
& ( member(esk12_2(X150,X151),X151)
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) )
& ( member(esk13_2(X150,X151),X151)
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) )
& ( member(esk14_2(X150,X151),X151)
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) )
& ( apply(X150,esk12_2(X150,X151),esk13_2(X150,X151))
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) )
& ( apply(X150,esk13_2(X150,X151),esk14_2(X150,X151))
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) )
& ( ~ apply(X150,esk12_2(X150,X151),esk14_2(X150,X151))
| ~ apply(X150,esk11_2(X150,X151),esk11_2(X150,X151))
| pre_order(X150,X151) ) ),
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)],[pre_order])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X159,X160] :
( pre_order(esk16_0,esk15_0)
& ( apply(esk16_0,X159,X160)
| ~ apply(esk17_0,X159,X160)
| ~ member(X159,esk15_0)
| ~ member(X160,esk15_0) )
& ( apply(esk16_0,X160,X159)
| ~ apply(esk17_0,X159,X160)
| ~ member(X159,esk15_0)
| ~ member(X160,esk15_0) )
& ( ~ apply(esk16_0,X159,X160)
| ~ apply(esk16_0,X160,X159)
| apply(esk17_0,X159,X160)
| ~ member(X159,esk15_0)
| ~ member(X160,esk15_0) )
& member(esk18_0,esk15_0)
& member(esk19_0,esk15_0)
& member(esk20_0,esk15_0)
& member(esk21_0,esk15_0)
& apply(esk17_0,esk18_0,esk20_0)
& apply(esk17_0,esk19_0,esk21_0)
& apply(esk16_0,esk18_0,esk19_0)
& ~ apply(esk16_0,esk20_0,esk21_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
cnf(c_0_5,plain,
( apply(X5,X1,X4)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X5,X1,X3)
| ~ apply(X5,X3,X4)
| ~ pre_order(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
apply(esk16_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( apply(esk16_0,X1,X2)
| ~ apply(esk17_0,X2,X1)
| ~ member(X2,esk15_0)
| ~ member(X1,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
apply(esk17_0,esk18_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
member(esk18_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
member(esk20_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( apply(esk16_0,X1,X2)
| ~ apply(esk17_0,X1,X2)
| ~ member(X1,esk15_0)
| ~ member(X2,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
apply(esk17_0,esk19_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
member(esk21_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
member(esk19_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( apply(esk16_0,X1,esk19_0)
| ~ pre_order(esk16_0,X2)
| ~ apply(esk16_0,X1,esk18_0)
| ~ member(esk19_0,X2)
| ~ member(esk18_0,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_16,negated_conjecture,
apply(esk16_0,esk20_0,esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_17,negated_conjecture,
apply(esk16_0,esk19_0,esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_18,negated_conjecture,
( apply(esk16_0,esk20_0,esk19_0)
| ~ pre_order(esk16_0,X1)
| ~ member(esk19_0,X1)
| ~ member(esk18_0,X1)
| ~ member(esk20_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
pre_order(esk16_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk16_0,X1,esk21_0)
| ~ pre_order(esk16_0,X2)
| ~ apply(esk16_0,X1,esk19_0)
| ~ member(esk21_0,X2)
| ~ member(esk19_0,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
apply(esk16_0,esk20_0,esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_9]),c_0_10])]) ).
cnf(c_0_22,negated_conjecture,
~ apply(esk16_0,esk20_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( ~ pre_order(esk16_0,X1)
| ~ member(esk21_0,X1)
| ~ member(esk19_0,X1)
| ~ member(esk20_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_13]),c_0_14]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET776+4 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.16/0.33 % Computer : n025.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:35:13 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.67/1.84 % Version : CSE_E---1.7
% 1.67/1.84 % Problem : theBenchmark.p
% 1.67/1.84 % SZS status Theorem for theBenchmark.p
% 1.67/1.84 % SZS output start CNFRefutation
% See solution above
% 1.67/1.84 % Total time : 1.369s
%------------------------------------------------------------------------------