%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS216+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n010.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 04:36:51 PM UTC 2026
% Result : Theorem 2.14s 1.94s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 30 ~; 26 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 5 sgn 39 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(completeness,axiom,
! [X9,X10] :
( model(X9,X10)
<~> model(X9,not(X10)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',completeness) ).
fof(contradiction,axiom,
? [X10] :
! [X9] : ~ model(X9,X10),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',contradiction) ).
fof(thm,axiom,
! [X1,X2] :
( ! [X3] :
( model(X3,X1)
=> model(X3,X2) )
<=> status(X1,X2,thm) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',thm) ).
fof(uns,axiom,
! [X1,X2] :
( ( ! [X3] : model(X3,X1)
& ! [X4] : model(X4,not(X2)) )
<=> status(X1,X2,uns) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+0.ax',uns) ).
fof(tautology,axiom,
? [X10] :
! [X9] : model(X9,X10),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',tautology) ).
fof(nota,axiom,
! [X7,X8] :
( ? [X1,X2] :
( status(X1,X2,X7)
& ~ status(X1,X2,X8) )
<=> nota(X7,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/KRS001+1.ax',nota) ).
fof(nota_uns_thm,conjecture,
nota(uns,thm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota_uns_thm) ).
fof(c_0_7,plain,
! [X9,X10] :
~ ( model(X9,X10)
<=> model(X9,not(X10)) ),
inference(fof_simplification,[status(thm)],[completeness]) ).
fof(c_0_8,plain,
? [X10] :
! [X9] : ~ model(X9,X10),
inference(fof_simplification,[status(thm)],[contradiction]) ).
fof(c_0_9,plain,
! [X167,X168,X170,X171,X172] :
( ( model(esk10_2(X167,X168),X167)
| status(X167,X168,thm) )
& ( ~ model(esk10_2(X167,X168),X168)
| status(X167,X168,thm) )
& ( ~ status(X170,X171,thm)
| ~ model(X172,X170)
| model(X172,X171) ) ),
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)],[thm])])])])])]) ).
fof(c_0_10,plain,
! [X337,X338] :
( ( ~ model(X337,X338)
| ~ model(X337,not(X338)) )
& ( model(X337,X338)
| model(X337,not(X338)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X347] : ~ model(X347,esk57_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
cnf(c_0_12,plain,
( status(X1,X2,thm)
| ~ model(esk10_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( model(X1,X2)
| model(X1,not(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
~ model(X1,esk57_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( status(X1,not(X2),thm)
| model(esk10_2(X1,not(X2)),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X279,X280,X283,X284,X285,X286] :
( ( ~ model(esk39_2(X279,X280),X279)
| ~ model(esk40_2(X279,X280),not(X280))
| status(X279,X280,uns) )
& ( model(X285,X283)
| ~ status(X283,X284,uns) )
& ( model(X286,not(X284))
| ~ status(X283,X284,uns) ) ),
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)],[uns])])])])])]) ).
fof(c_0_17,plain,
! [X342] : model(X342,esk53_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[tautology])]) ).
cnf(c_0_18,plain,
( model(X3,X2)
| ~ status(X1,X2,thm)
| ~ model(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
status(X1,not(esk57_0),thm),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X7,X8] :
( ? [X1,X2] :
( status(X1,X2,X7)
& ~ status(X1,X2,X8) )
<=> nota(X7,X8) ),
inference(fof_simplification,[status(thm)],[nota]) ).
cnf(c_0_21,plain,
( status(X1,X2,uns)
| ~ model(esk39_2(X1,X2),X1)
| ~ model(esk40_2(X1,X2),not(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
model(X1,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( model(X1,not(esk57_0))
| ~ model(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X311,X312,X313,X314,X315,X316] :
( ( ~ status(X313,X314,X311)
| status(X313,X314,X312)
| nota(X311,X312) )
& ( status(esk47_2(X315,X316),esk48_2(X315,X316),X315)
| ~ nota(X315,X316) )
& ( ~ status(esk47_2(X315,X316),esk48_2(X315,X316),X316)
| ~ nota(X315,X316) ) ),
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)],[c_0_20])])])])])]) ).
cnf(c_0_25,plain,
( status(esk53_0,X1,uns)
| ~ model(esk40_2(esk53_0,X1),not(X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
model(X1,not(esk57_0)),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
fof(c_0_27,negated_conjecture,
~ nota(uns,thm),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nota_uns_thm])]) ).
cnf(c_0_28,plain,
( status(X1,X2,X4)
| nota(X3,X4)
| ~ status(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
status(esk53_0,esk57_0,uns),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ nota(uns,thm),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( nota(uns,X1)
| status(esk53_0,esk57_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
status(esk53_0,esk57_0,thm),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_22])]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS216+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n010.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:40:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.14/1.94 % Version : CSE_E---1.7
% 2.14/1.94 % Problem : theBenchmark.p
% 2.14/1.94 % SZS status Theorem for theBenchmark.p
% 2.14/1.94 % SZS output start CNFRefutation
% See solution above
% 2.14/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------