%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN050+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:36:51 AM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 51 ( 16 ~; 11 |; 18 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 44 ( 6 sgn 26 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel20,conjecture,
( ! [X,Y] :
? [Z] :
! [W] :
( ( big_q(Y)
& big_p(X) )
=> ( big_s(W)
& big_r(Z) ) )
=> ? [X1,Y1] :
( ( big_q(Y1)
& big_p(X1) )
=> ? [Z1] : big_r(Z1) ) ),
file('theBenchmark.p',pel20) ).
fof(pel20_neg,negated_conjecture,
~ ( ! [X,Y] :
? [Z] :
! [W] :
( ( big_q(Y)
& big_p(X) )
=> ( big_s(W)
& big_r(Z) ) )
=> ? [X1,Y1] :
( ( big_q(Y1)
& big_p(X1) )
=> ? [Z1] : big_r(Z1) ) ),
inference(assume_negation,[status(cth)],[pel20]) ).
fof(nnf_1,plain,
( ! [X1,Y1] :
( ! [Z1] : ~ big_r(Z1)
& big_q(Y1)
& big_p(X1) )
& ! [X,Y] :
? [Z] :
! [W] :
( ( big_s(W)
& big_r(Z) )
| ~ big_q(Y)
| ~ big_p(X) ) ),
inference(fof_nnf,[status(thm)],[pel20_neg]) ).
fof(sk_pel20_neg_sk,plain,
( ! [X1,Y1] :
( ! [Z1] : ~ big_r(Z1)
& big_q(Y1)
& big_p(X1) )
& ! [X,Y,W] :
( ( big_s(W)
& big_r(sK0(X,Y)) )
| ~ big_q(Y)
| ~ big_p(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_pel20_neg,plain,
( ! [VAR_0] : ~ big_r(VAR_0)
& ! [VAR_0] : big_q(VAR_0)
& ! [VAR_0] : big_p(VAR_0)
& ! [VAR_0,VAR_1,VAR_2] :
( big_s(VAR_2)
| ~ big_q(VAR_1)
| ~ big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_r(sK0(VAR_0,VAR_1))
| ~ big_q(VAR_1)
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel20_neg_sk]) ).
cnf(c_2,negated_conjecture,
big_p(A),
inference(split_conjunct,[status(thm)],[sk_pel20_neg]) ).
cnf(c_4,negated_conjecture,
( big_r(sK0(A,B))
| ~ big_q(B)
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_pel20_neg]) ).
cnf(c_5,negated_conjecture,
big_q(A),
inference(split_conjunct,[status(thm)],[sk_pel20_neg]) ).
cnf(c_7,negated_conjecture,
( big_r(sK0(B,A))
| ~ big_q(A) ),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_8,negated_conjecture,
~ big_r(A),
inference(split_conjunct,[status(thm)],[sk_pel20_neg]) ).
cnf(c_9,negated_conjecture,
big_r(sK0(A,B)),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_10,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_8,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN050+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:06:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3216852 was started by sandbox2 on n013,
% 0.09/0.36 % Sat Sep 26 17:06:21 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 8.
% 0.09/0.37 % Level of proof is 4.
% 0.09/0.37 % Maximum clause weight is 0.000.
% 0.09/0.37 % Given clauses 0.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------