%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:39:12 AM UTC 2026
% Result : Theorem 0.13s 5.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 109 ( 40 ~; 45 |; 18 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm31,conjecture,
( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
file('theBenchmark.p',thm31) ).
fof(thm31_neg,negated_conjecture,
~ ( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
inference(assume_negation,[status(cth)],[thm31]) ).
fof(nnf_1,plain,
( ( ? [X] :
( ( ~ r(X)
| ~ s(X)
| ~ r(X) )
& ( r(X)
| ( s(X)
& r(X) ) ) )
| ? [X2] :
( ~ s(X2)
& r(X2) ) )
& ( ! [X1] :
( ( ~ r(X1)
| ( s(X1)
& r(X1) ) )
& ( r(X1)
| ~ s(X1)
| ~ r(X1) ) )
| ! [X0] :
( s(X0)
| ~ r(X0) ) ) ),
inference(fof_nnf,[status(thm)],[thm31_neg]) ).
fof(sk_thm31_neg_sk,plain,
( ( ( ( ~ r(sK1)
| ~ s(sK1)
| ~ r(sK1) )
& ( r(sK1)
| ( s(sK1)
& r(sK1) ) ) )
| ( ~ s(sK0)
& r(sK0) ) )
& ( ! [X1] :
( ( ~ r(X1)
| ( s(X1)
& r(X1) ) )
& ( r(X1)
| ~ s(X1)
| ~ r(X1) ) )
| ! [X0] :
( s(X0)
| ~ r(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X,sK1)],[nnf_1]) ).
fof(sk_thm31_neg,plain,
( ( ~ s(sK1)
| ~ r(sK1)
| ~ s(sK0) )
& ( r(sK1)
| ~ s(sK0) )
& ( ~ s(sK1)
| ~ r(sK1)
| r(sK0) )
& ( r(sK1)
| r(sK0) )
& ! [VAR_0,VAR_1] :
( ~ r(VAR_1)
| s(VAR_1)
| s(VAR_0)
| ~ r(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_thm31_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ r(B)
| s(B)
| s(A)
| ~ r(A) ),
inference(split_conjunct,[status(thm)],[sk_thm31_neg]) ).
cnf(c_3,negated_conjecture,
( r(sK1)
| r(sK0) ),
inference(split_conjunct,[status(thm)],[sk_thm31_neg]) ).
cnf(c_4,negated_conjecture,
( ~ s(sK1)
| ~ r(sK1)
| r(sK0) ),
inference(split_conjunct,[status(thm)],[sk_thm31_neg]) ).
cnf(c_5,negated_conjecture,
( r(sK1)
| ~ s(sK0) ),
inference(split_conjunct,[status(thm)],[sk_thm31_neg]) ).
cnf(c_6,negated_conjecture,
( ~ s(sK1)
| ~ r(sK1)
| ~ s(sK0) ),
inference(split_conjunct,[status(thm)],[sk_thm31_neg]) ).
cnf(c_17,plain,
( s(A)
| s(A)
| ~ r(A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_7,plain,
( s(A)
| ~ r(A) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_8,plain,
( r(sK0)
| s(sK1) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_18,negated_conjecture,
( ~ r(sK1)
| r(sK0)
| r(sK0) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_10,negated_conjecture,
( ~ r(sK1)
| r(sK0) ),
inference(copy,[status(thm)],[c_18]) ).
cnf(c_19,negated_conjecture,
( r(sK0)
| r(sK0) ),
inference(resolve,[status(thm)],[c_10,c_3]) ).
cnf(c_11,negated_conjecture,
r(sK0),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_12,plain,
s(sK0),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_13,negated_conjecture,
( ~ s(sK1)
| ~ r(sK1) ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_14,negated_conjecture,
r(sK1),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_15,negated_conjecture,
~ s(sK1),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_20,negated_conjecture,
s(sK1),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_16,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_15,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n020.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sat Sep 26 18:22:56 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.42 % Process 2238182 was started by sandbox on n020,
% 0.13/5.42 % Sat Sep 26 18:22:56 2026
% 0.13/5.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/5.42
% 0.13/5.42 % From the command line: assign(max_seconds, 300).
% 0.13/5.44
% 0.13/5.44 % SZS status Theorem for theBenchmark
% 0.13/5.44
% 0.13/5.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/5.44 % Length of proof is 15.
% 0.13/5.44 % Level of proof is 9.
% 0.13/5.44 % Maximum clause weight is 8.000.
% 0.13/5.44 % Given clauses 10.
% 0.13/5.44
% 0.13/5.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------