%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET804+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 : n026.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 05:08:31 PM UTC 2026
% Result : Theorem 1.28s 1.71s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 80 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 90 ( 34 ~; 30 |; 18 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 2 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV16,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( min(X8,X1,X2)
& min(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV16) ).
fof(min,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X3,X6) )
=> X6 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).
fof(least,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( min(X8,X1,X2)
& min(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIV16]) ).
fof(c_0_4,plain,
! [X111,X112,X113,X114,X115,X116,X117] :
( ( member(X113,X112)
| ~ min(X113,X111,X112) )
& ( ~ member(X114,X112)
| ~ apply(X111,X114,X113)
| X113 = X114
| ~ min(X113,X111,X112) )
& ( member(esk8_3(X115,X116,X117),X116)
| ~ member(X117,X116)
| min(X117,X115,X116) )
& ( apply(X115,esk8_3(X115,X116,X117),X117)
| ~ member(X117,X116)
| min(X117,X115,X116) )
& ( X117 != esk8_3(X115,X116,X117)
| ~ member(X117,X116)
| min(X117,X115,X116) ) ),
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)],[min])])])])])]) ).
fof(c_0_5,negated_conjecture,
( order(esk11_0,esk12_0)
& min(esk13_0,esk11_0,esk12_0)
& min(esk14_0,esk11_0,esk12_0)
& esk13_0 != esk14_0
& least(esk15_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X95,X96,X97,X98,X99,X100,X101] :
( ( member(X97,X96)
| ~ least(X97,X95,X96) )
& ( ~ member(X98,X96)
| apply(X95,X97,X98)
| ~ least(X97,X95,X96) )
& ( member(esk6_3(X99,X100,X101),X100)
| ~ member(X101,X100)
| least(X101,X99,X100) )
& ( ~ apply(X99,X101,esk6_3(X99,X100,X101))
| ~ member(X101,X100)
| least(X101,X99,X100) ) ),
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)],[least])])])])])]) ).
cnf(c_0_7,plain,
( X4 = X1
| ~ member(X1,X2)
| ~ apply(X3,X1,X4)
| ~ min(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
min(esk14_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ least(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
least(esk15_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ least(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ min(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk14_0
| ~ apply(esk11_0,X1,esk14_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( apply(esk11_0,esk15_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk15_0,esk12_0),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
member(esk14_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_17,negated_conjecture,
min(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
esk15_0 = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk13_0
| ~ apply(esk11_0,X1,esk13_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk11_0,esk14_0,X1)
| ~ member(X1,esk12_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET804+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.10 % 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
% 0.14/0.31 % Computer : n026.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 02:36:08 EDT 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.71 % Version : CSE_E---1.7
% 1.28/1.71 % Problem : theBenchmark.p
% 1.28/1.71 % SZS status Theorem for theBenchmark.p
% 1.28/1.71 % SZS output start CNFRefutation
% See solution above
% 1.28/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------