%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN369+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 : n020.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 09:37:43 AM UTC 2026
% Result : Theorem 0.08s 5.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 3 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 13 ( 4 ~; 5 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 25 ( 4 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2120,conjecture,
( ! [U,V,W] :
( big_p(V,W)
| big_p(U,V) )
=> ? [X] :
! [Y] : big_p(X,Y) ),
file('theBenchmark.p',x2120) ).
fof(x2120_neg,negated_conjecture,
~ ( ! [U,V,W] :
( big_p(V,W)
| big_p(U,V) )
=> ? [X] :
! [Y] : big_p(X,Y) ),
inference(assume_negation,[status(cth)],[x2120]) ).
fof(nnf_1,plain,
( ! [X] :
? [Y] : ~ big_p(X,Y)
& ! [U,V,W] :
( big_p(V,W)
| big_p(U,V) ) ),
inference(fof_nnf,[status(thm)],[x2120_neg]) ).
fof(sk_x2120_neg,plain,
( ! [X] : ~ big_p(X,sK0(X))
& ! [U,V,W] :
( big_p(V,W)
| big_p(U,V) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( big_p(B,C)
| big_p(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2120_neg]) ).
cnf(c_3,negated_conjecture,
~ big_p(A,sK0(A)),
inference(split_conjunct,[status(thm)],[sk_x2120_neg]) ).
cnf(c_5,plain,
big_p(A,B),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_6,plain,
$false,
inference(resolve,[status(thm)],[c_5,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN369+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n020.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 17:39:25 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 2138799 was started by sandbox2 on n020,
% 0.08/5.37 % Sat Sep 26 17:39:25 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 0.08/5.37
% 0.08/5.37 % SZS status Theorem for theBenchmark
% 0.08/5.37
% 0.08/5.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/5.37 % Length of proof is 5.
% 0.08/5.37 % Level of proof is 3.
% 0.08/5.37 % Maximum clause weight is 6.000.
% 0.08/5.37 % Given clauses 2.
% 0.08/5.37
% 0.08/5.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------