%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:43:28 AM UTC 2026
% Result : Theorem 0.18s 5.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 3 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 42 ( 13 ~; 11 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 41 ( 6 sgn 21 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
! [Z,Y] :
( ( ~ p(Y,sK0(Z))
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,sK0(Z)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(Z))],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ p(VAR_1,sK0(VAR_2))
| ~ p(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( p(VAR_1,VAR_2)
| ~ p(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( p(VAR_2,VAR_1)
| ~ p(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( p(VAR_0,VAR_1)
| p(VAR_0,sK0(VAR_1)) )
& ! [VAR_0,VAR_1] :
( p(VAR_1,VAR_0)
| p(VAR_0,sK0(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( p(B,A)
| p(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( p(C,B)
| ~ p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( ~ p(B,sK0(C))
| ~ p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,plain,
~ p(sK0(A),sK0(A)),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_9,plain,
( p(B,sK0(C))
| p(A,B) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_12,plain,
p(sK0(A),sK0(A)),
inference(factor,[status(thm)],[c_9]) ).
cnf(c_11,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n015.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 18:55:34 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 527751 was started by sandbox on n015,
% 0.18/5.46 % Sat Sep 26 18:55:34 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 0.18/5.48
% 0.18/5.48 % SZS status Theorem for theBenchmark
% 0.18/5.48
% 0.18/5.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.48 % Length of proof is 7.
% 0.18/5.48 % Level of proof is 3.
% 0.18/5.48 % Maximum clause weight is 7.000.
% 0.18/5.48 % Given clauses 3.
% 0.18/5.48
% 0.18/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------