%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:07:35 AM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 89 ( 41 ~; 28 |; 10 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 57 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l12_induction,axiom,
( ! [U,V,W,X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ( ~ ok(triple(X,Y,Z))
=> ~ ok(im_succ_cpq(triple(X,Y,Z))) ) )
=> ! [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('theBenchmark.p',l12_induction) ).
fof(l12_l13,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(im_succ_cpq(triple(U,V,W))) ),
file('theBenchmark.p',l12_l13) ).
fof(l12_co,conjecture,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ~ ok(triple(X,Y,Z)) ) ),
file('theBenchmark.p',l12_co) ).
fof(l12_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ! [X,Y,Z] :
( succ_cpq(triple(U,V,W),triple(X,Y,Z))
=> ~ ok(triple(X,Y,Z)) ) ),
inference(assume_negation,[status(cth)],[l12_co]) ).
fof(nnf_41,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ok(triple(X1,X2,X3)) )
| ? [U,V,W,X,Y,Z] :
( ok(im_succ_cpq(triple(X,Y,Z)))
& ~ ok(triple(X,Y,Z))
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) ) ),
inference(fof_nnf,[status(thm)],[l12_induction]) ).
fof(sk_l12_induction_sk,plain,
( ! [X1,X2,X3] :
( ! [X4,X5,X6] :
( ~ ok(triple(X4,X5,X6))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6)) )
| ok(triple(X1,X2,X3)) )
| ( ok(im_succ_cpq(triple(sK0,sK1,sK2)))
& ~ ok(triple(sK0,sK1,sK2))
& succ_cpq(triple(sK9,sK10,sK11),triple(sK0,sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK0,sK1,sK2]),skolemize(U,sK9),skolemize(V,sK10),skolemize(W,sK11),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_41]) ).
fof(sk_l12_induction,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ ok(triple(VAR_3,VAR_4,VAR_5))
| ~ succ_cpq(triple(VAR_0,VAR_1,VAR_2),triple(VAR_3,VAR_4,VAR_5))
| ok(triple(VAR_0,VAR_1,VAR_2))
| ok(im_succ_cpq(triple(sK0,sK1,sK2))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ ok(triple(VAR_3,VAR_4,VAR_5))
| ~ succ_cpq(triple(VAR_0,VAR_1,VAR_2),triple(VAR_3,VAR_4,VAR_5))
| ok(triple(VAR_0,VAR_1,VAR_2))
| ~ ok(triple(sK0,sK1,sK2)) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ ok(triple(VAR_3,VAR_4,VAR_5))
| ~ succ_cpq(triple(VAR_0,VAR_1,VAR_2),triple(VAR_3,VAR_4,VAR_5))
| ok(triple(VAR_0,VAR_1,VAR_2))
| succ_cpq(triple(sK9,sK10,sK11),triple(sK0,sK1,sK2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_l12_induction_sk]) ).
cnf(c_100,plain,
( ~ ok(triple(D,E,F))
| ~ succ_cpq(triple(A,B,C),triple(D,E,F))
| ok(triple(A,B,C))
| ~ ok(triple(sK0,sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_l12_induction]) ).
cnf(c_101,plain,
( ~ ok(triple(D,E,F))
| ~ succ_cpq(triple(A,B,C),triple(D,E,F))
| ok(triple(A,B,C))
| ok(im_succ_cpq(triple(sK0,sK1,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_l12_induction]) ).
cnf(c_102,plain,
( ~ ok(im_succ_cpq(triple(A,B,C)))
| ok(triple(A,B,C)) ),
inference(clausify,[status(thm)],[l12_l13]) ).
fof(nnf_43,plain,
? [U,V,W] :
( ? [X,Y,Z] :
( ok(triple(X,Y,Z))
& succ_cpq(triple(U,V,W),triple(X,Y,Z)) )
& ~ ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l12_co_neg]) ).
fof(sk_l12_co_neg,plain,
( ok(triple(sK6,sK7,sK8))
& succ_cpq(triple(sK3,sK4,sK5),triple(sK6,sK7,sK8))
& ~ ok(triple(sK3,sK4,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(U,sK3),skolemize(V,sK4),skolemize(W,sK5),skolemize(X,sK6),skolemize(Y,sK7),skolemize(Z,sK8)],[nnf_43]) ).
cnf(c_103,negated_conjecture,
~ ok(triple(sK3,sK4,sK5)),
inference(split_conjunct,[status(thm)],[sk_l12_co_neg]) ).
cnf(c_104,negated_conjecture,
succ_cpq(triple(sK3,sK4,sK5),triple(sK6,sK7,sK8)),
inference(split_conjunct,[status(thm)],[sk_l12_co_neg]) ).
cnf(c_105,negated_conjecture,
ok(triple(sK6,sK7,sK8)),
inference(split_conjunct,[status(thm)],[sk_l12_co_neg]) ).
cnf(c_290,negated_conjecture,
( ~ ok(triple(sK6,sK7,sK8))
| ok(triple(sK3,sK4,sK5))
| ok(im_succ_cpq(triple(sK0,sK1,sK2))) ),
inference(resolve,[status(thm)],[c_104,c_101]) ).
cnf(c_291,negated_conjecture,
( ~ ok(triple(sK6,sK7,sK8))
| ok(im_succ_cpq(triple(sK0,sK1,sK2))) ),
inference(resolve,[status(thm)],[c_103,c_290]) ).
cnf(c_238,negated_conjecture,
ok(im_succ_cpq(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_105,c_291]) ).
cnf(c_292,negated_conjecture,
( ~ ok(triple(sK6,sK7,sK8))
| ok(triple(sK3,sK4,sK5))
| ~ ok(triple(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_104,c_100]) ).
cnf(c_293,negated_conjecture,
( ~ ok(triple(sK6,sK7,sK8))
| ~ ok(triple(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_103,c_292]) ).
cnf(c_239,negated_conjecture,
~ ok(triple(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_105,c_293]) ).
cnf(c_294,plain,
~ ok(im_succ_cpq(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_102,c_239]) ).
cnf(c_289,plain,
$false,
inference(resolve,[status(thm)],[c_238,c_294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 13:42:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1131071 was started by sandbox2 on n026,
% 0.10/0.37 % Sat Sep 26 13:42:10 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.44 % Length of proof is 12.
% 0.15/0.44 % Level of proof is 3.
% 0.15/0.44 % Maximum clause weight is 40.000.
% 0.15/0.44 % Given clauses 63.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------