%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV376+1 : TPTP v9.2.1. Released v3.3.0.
% 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 05:22:02 PM UTC 2026
% Result : Theorem 1.13s 1.61s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 75 ( 6 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 87 ( 42 ~; 22 |; 4 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 92 ( 4 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l12_co,conjecture,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ~ ok(triple(X4,X5,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_co) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(l12_induction,axiom,
( ! [X1,X2,X3,X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
=> ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
=> ! [X7,X8,X9] :
( ~ ok(triple(X7,X8,X9))
=> ! [X10,X11,X12] :
( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
=> ~ ok(triple(X10,X11,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_induction) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(l12_l13,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_l13) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ~ ok(triple(X4,X5,X6)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l12_co])]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(c_0_7,negated_conjecture,
( ~ ok(triple(esk7_0,esk8_0,esk9_0))
& succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0))
& ok(triple(esk10_0,esk11_0,esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X227,X228,X229] :
( ok(triple(X227,X228,X229))
| X229 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_9,plain,
( ! [X1,X2,X3,X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
=> ~ ok(im_succ_cpq(triple(X4,X5,X6))) ) )
=> ! [X7,X8,X9] :
( ~ ok(triple(X7,X8,X9))
=> ! [X10,X11,X12] :
( succ_cpq(triple(X7,X8,X9),triple(X10,X11,X12))
=> ~ ok(triple(X10,X11,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[l12_induction]) ).
cnf(c_0_10,negated_conjecture,
~ ok(triple(esk7_0,esk8_0,esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(c_0_13,plain,
! [X270,X271,X272,X273,X274,X275] :
( ( succ_cpq(triple(esk1_0,esk2_0,esk3_0),triple(esk4_0,esk5_0,esk6_0))
| ok(triple(X270,X271,X272))
| ~ succ_cpq(triple(X270,X271,X272),triple(X273,X274,X275))
| ~ ok(triple(X273,X274,X275)) )
& ( ~ ok(triple(esk4_0,esk5_0,esk6_0))
| ok(triple(X270,X271,X272))
| ~ succ_cpq(triple(X270,X271,X272),triple(X273,X274,X275))
| ~ ok(triple(X273,X274,X275)) )
& ( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
| ok(triple(X270,X271,X272))
| ~ succ_cpq(triple(X270,X271,X272),triple(X273,X274,X275))
| ~ ok(triple(X273,X274,X275)) ) ),
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_9])])])])]) ).
cnf(c_0_14,negated_conjecture,
succ_cpq(triple(esk7_0,esk8_0,esk9_0),triple(esk10_0,esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
esk9_0 = bad,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,plain,
! [X225,X226] : ~ ok(triple(X225,X226,bad)),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ok(triple(X1,X2,X3))
| ~ ok(triple(esk4_0,esk5_0,esk6_0))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
succ_cpq(triple(esk7_0,esk8_0,bad),triple(esk10_0,esk11_0,esk12_0)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
ok(triple(esk10_0,esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ ok(triple(esk4_0,esk5_0,esk6_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
fof(c_0_22,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[l12_l13]) ).
cnf(c_0_23,plain,
( ok(im_succ_cpq(triple(esk4_0,esk5_0,esk6_0)))
| ok(triple(X1,X2,X3))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
esk6_0 = bad,
inference(spm,[status(thm)],[c_0_21,c_0_11]) ).
fof(c_0_25,lemma,
! [X276,X277,X278] :
( ok(triple(X276,X277,X278))
| ~ ok(im_succ_cpq(triple(X276,X277,X278))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])]) ).
cnf(c_0_26,plain,
( ok(im_succ_cpq(triple(esk4_0,esk5_0,bad)))
| ok(triple(X1,X2,X3))
| ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,lemma,
( ok(triple(X1,X2,X3))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
ok(im_succ_cpq(triple(esk4_0,esk5_0,bad))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_29,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWV376+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 00:04:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.61 % Version : CSE_E---1.7
% 1.13/1.61 % Problem : theBenchmark.p
% 1.13/1.61 % SZS status Theorem for theBenchmark.p
% 1.13/1.61 % SZS output start CNFRefutation
% See solution above
% 1.13/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------