%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN380+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 : n006.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 09:37:45 AM UTC 2026
% Result : Theorem 0.08s 10.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 6 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 27 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2132,conjecture,
( ! [W] : ~ big_r(W,W)
=> ? [X,Y] :
( ( big_q(Y,X)
=> ! [Z] : big_q(Z,Z) )
& ~ big_r(X,Y) ) ),
file('theBenchmark.p',x2132) ).
fof(x2132_neg,negated_conjecture,
~ ( ! [W] : ~ big_r(W,W)
=> ? [X,Y] :
( ( big_q(Y,X)
=> ! [Z] : big_q(Z,Z) )
& ~ big_r(X,Y) ) ),
inference(assume_negation,[status(cth)],[x2132]) ).
fof(nnf_1,plain,
( ! [X,Y] :
( ( ? [Z] : ~ big_q(Z,Z)
& big_q(Y,X) )
| big_r(X,Y) )
& ! [W] : ~ big_r(W,W) ),
inference(fof_nnf,[status(thm)],[x2132_neg]) ).
fof(sk_x2132_neg_sk,plain,
( ! [X,Y] :
( ( ~ big_q(sK0(X,Y),sK0(X,Y))
& big_q(Y,X) )
| big_r(X,Y) )
& ! [W] : ~ big_r(W,W) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_x2132_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_q(sK0(VAR_0,VAR_1),sK0(VAR_0,VAR_1))
| big_r(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( big_q(VAR_1,VAR_0)
| big_r(VAR_0,VAR_1) )
& ! [VAR_0] : ~ big_r(VAR_0,VAR_0) ),
inference(cnf_transformation,[status(thm)],[sk_x2132_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_q(B,A)
| big_r(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2132_neg]) ).
cnf(c_3,negated_conjecture,
~ big_r(A,A),
inference(split_conjunct,[status(thm)],[sk_x2132_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_q(sK0(A,B),sK0(A,B))
| big_r(A,B) ),
inference(split_conjunct,[status(thm)],[sk_x2132_neg]) ).
cnf(c_5,negated_conjecture,
big_q(A,A),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
~ big_q(sK0(A,A),sK0(A,A)),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_7,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN380+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n006.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sat Sep 26 17:39:23 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.38 % Process 1799285 was started by sandbox2 on n006,
% 0.08/10.38 % Sat Sep 26 17:39:23 2026
% 0.08/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.08/10.39
% 0.08/10.39 % SZS status Theorem for theBenchmark
% 0.08/10.39
% 0.08/10.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/10.39 % Length of proof is 7.
% 0.08/10.39 % Level of proof is 3.
% 0.08/10.39 % Maximum clause weight is 0.000.
% 0.08/10.39 % Given clauses 0.
% 0.08/10.39
% 0.08/10.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------