%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:43:24 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 106 ( 45 ~; 39 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 42 ( 12 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [C,B] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( r(Y)
=> ( r(C)
& r(B) ) )
& ( p(f(Y))
=> p(X) ) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [C,B] :
( ! [Z] : q(f(Z))
=> ? [X,Y] :
( q(X)
& ( r(Y)
=> ( r(C)
& r(B) ) )
& ( p(f(Y))
=> p(X) ) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [C,B] :
( ! [X,Y] :
( ~ q(X)
| ( ( ~ r(C)
| ~ r(B) )
& r(Y) )
| ( ~ p(X)
& p(f(Y)) ) )
& ! [Z] : q(f(Z)) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ! [X,Y] :
( ~ q(X)
| ( ( ~ r(sK1)
| ~ r(sK0) )
& r(Y) )
| ( ~ p(X)
& p(f(Y)) ) )
& ! [Z] : q(f(Z)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(C,sK1),skolemize(B,sK0)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0] :
( ~ q(VAR_0)
| ~ r(sK1)
| ~ r(sK0)
| ~ p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ q(VAR_0)
| r(VAR_1)
| ~ p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ q(VAR_1)
| ~ r(sK1)
| ~ r(sK0)
| p(f(VAR_0)) )
& ! [VAR_0,VAR_1] :
( ~ q(VAR_1)
| r(VAR_0)
| p(f(VAR_0)) )
& ! [VAR_0] : q(f(VAR_0)) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ q(B)
| r(A)
| p(f(A)) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
q(f(A)),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( ~ q(B)
| ~ r(sK1)
| ~ r(sK0)
| p(f(A)) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( ~ q(A)
| r(B)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( ~ q(A)
| ~ r(sK1)
| ~ r(sK0)
| ~ p(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0)
| p(f(A)) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_8,negated_conjecture,
( r(B)
| ~ p(f(A)) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_9,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0)
| ~ p(f(A)) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_10,negated_conjecture,
( r(A)
| p(f(A)) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_11,negated_conjecture,
( r(B)
| r(A) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_12,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0)
| ~ r(sK1)
| ~ r(sK0) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_16,negated_conjecture,
( ~ r(sK1)
| ~ r(sK1)
| ~ r(sK0) ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_13,negated_conjecture,
( ~ r(sK1)
| ~ r(sK0) ),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_14,plain,
r(A),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_17,negated_conjecture,
~ r(sK1),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_15,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_14,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN939+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 18:51:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2849325 was started by sandbox2 on n005,
% 0.08/0.35 % Sat Sep 26 18:51:02 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 15.
% 0.08/0.37 % Level of proof is 5.
% 0.08/0.37 % Maximum clause weight is 4.000.
% 0.08/0.37 % Given clauses 0.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------