%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET794+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 : n024.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 05:08:30 PM UTC 2026
% Result : Theorem 1.13s 1.64s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 111 ( 7 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 126 ( 42 ~; 55 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 1 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV6,conjecture,
! [X1,X2,X6] :
( ( total_order(X1,X2)
& min(X6,X1,X2) )
=> least(X6,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV6) ).
fof(total_order,axiom,
! [X1,X2] :
( total_order(X1,X2)
<=> ( order(X1,X2)
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( apply(X1,X3,X4)
| apply(X1,X4,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',total_order) ).
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/sandbox/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/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X6] :
( ( total_order(X1,X2)
& min(X6,X1,X2) )
=> least(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thIV6]) ).
fof(c_0_5,plain,
! [X59,X60,X61,X62,X63,X64] :
( ( order(X59,X60)
| ~ total_order(X59,X60) )
& ( ~ member(X61,X60)
| ~ member(X62,X60)
| apply(X59,X61,X62)
| apply(X59,X62,X61)
| ~ total_order(X59,X60) )
& ( member(esk1_2(X63,X64),X64)
| ~ order(X63,X64)
| total_order(X63,X64) )
& ( member(esk2_2(X63,X64),X64)
| ~ order(X63,X64)
| total_order(X63,X64) )
& ( ~ apply(X63,esk1_2(X63,X64),esk2_2(X63,X64))
| ~ order(X63,X64)
| total_order(X63,X64) )
& ( ~ apply(X63,esk2_2(X63,X64),esk1_2(X63,X64))
| ~ order(X63,X64)
| total_order(X63,X64) ) ),
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)],[total_order])])])])])]) ).
fof(c_0_6,negated_conjecture,
( total_order(esk11_0,esk12_0)
& min(esk13_0,esk11_0,esk12_0)
& ~ least(esk13_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X107,X108,X109,X110,X111,X112,X113] :
( ( member(X109,X108)
| ~ min(X109,X107,X108) )
& ( ~ member(X110,X108)
| ~ apply(X107,X110,X109)
| X109 = X110
| ~ min(X109,X107,X108) )
& ( member(esk8_3(X111,X112,X113),X112)
| ~ member(X113,X112)
| min(X113,X111,X112) )
& ( apply(X111,esk8_3(X111,X112,X113),X113)
| ~ member(X113,X112)
| min(X113,X111,X112) )
& ( X113 != esk8_3(X111,X112,X113)
| ~ member(X113,X112)
| min(X113,X111,X112) ) ),
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])])])])])]) ).
cnf(c_0_8,plain,
( apply(X4,X1,X3)
| apply(X4,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ total_order(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
total_order(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,X2)
| ~ min(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
min(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X91,X92,X93,X94,X95,X96,X97] :
( ( member(X93,X92)
| ~ least(X93,X91,X92) )
& ( ~ member(X94,X92)
| apply(X91,X93,X94)
| ~ least(X93,X91,X92) )
& ( member(esk6_3(X95,X96,X97),X96)
| ~ member(X97,X96)
| least(X97,X95,X96) )
& ( ~ apply(X95,X97,esk6_3(X95,X96,X97))
| ~ member(X97,X96)
| least(X97,X95,X96) ) ),
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_13,negated_conjecture,
( apply(esk11_0,X1,X2)
| apply(esk11_0,X2,X1)
| ~ member(X2,esk12_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( member(esk6_3(X1,X2,X3),X2)
| least(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( X4 = X1
| ~ member(X1,X2)
| ~ apply(X3,X1,X4)
| ~ min(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( apply(esk11_0,esk13_0,X1)
| apply(esk11_0,X1,esk13_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( least(esk13_0,X1,esk12_0)
| member(esk6_3(X1,esk12_0,esk13_0),esk12_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
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_16,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( least(esk13_0,X1,esk12_0)
| apply(esk11_0,esk6_3(X1,esk12_0,esk13_0),esk13_0)
| apply(esk11_0,esk13_0,esk6_3(X1,esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( least(X2,X1,X3)
| ~ apply(X1,X2,esk6_3(X1,X3,X2))
| ~ member(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( esk6_3(X1,esk12_0,esk13_0) = esk13_0
| least(esk13_0,X1,esk12_0)
| apply(esk11_0,esk13_0,esk6_3(X1,esk12_0,esk13_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ least(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
esk6_3(esk11_0,esk12_0,esk13_0) = esk13_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14])]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
apply(esk11_0,esk13_0,esk13_0),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_26,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_21,c_0_24]),c_0_25]),c_0_14])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET794+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.06/0.27 % Computer : n024.cluster.edu
% 0.06/0.27 % Model : x86_64 x86_64
% 0.06/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.27 % Memory : 8042.1875MB
% 0.06/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Mon May 4 21:34:56 EDT 2026
% 0.06/0.27 % CPUTime :
% 0.06/0.27 % start to proof: theBenchmark
% 1.13/1.64 % Version : CSE_E---1.7
% 1.13/1.64 % Problem : theBenchmark.p
% 1.13/1.64 % SZS status Theorem for theBenchmark.p
% 1.13/1.64 % SZS output start CNFRefutation
% See solution above
% 1.13/1.64 % Total time : 1.361s
%------------------------------------------------------------------------------