%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN072+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 09:36:57 AM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 56 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 12 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 5 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel49_1,axiom,
? [X,Y] :
! [Z] :
( Z = Y
| Z = X ),
file('theBenchmark.p',pel49_1) ).
fof(pel49,conjecture,
! [X] : big_p(X),
file('theBenchmark.p',pel49) ).
fof(pel49_neg,negated_conjecture,
~ ! [X] : big_p(X),
inference(assume_negation,[status(cth)],[pel49]) ).
fof(nnf_1,plain,
? [X,Y] :
! [Z] :
( Y = Z
| X = Z ),
inference(fof_nnf,[status(thm)],[pel49_1]) ).
fof(sk_pel49_1,plain,
! [Z] :
( sK1 = Z
| sK0 = Z ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_1]) ).
cnf(c_3,plain,
( sK1 = A
| sK0 = A ),
inference(split_conjunct,[status(thm)],[sk_pel49_1]) ).
fof(pel49_2,axiom,
big_p(a),
file('theBenchmark.p',pel49_2) ).
cnf(c_4,plain,
big_p(a),
inference(clausify,[status(thm)],[pel49_2]) ).
fof(pel49_3,axiom,
big_p(b),
file('theBenchmark.p',pel49_3) ).
cnf(c_5,plain,
big_p(b),
inference(clausify,[status(thm)],[pel49_3]) ).
fof(pel49_4,axiom,
a != b,
file('theBenchmark.p',pel49_4) ).
cnf(c_6,plain,
a != b,
inference(clausify,[status(thm)],[pel49_4]) ).
cnf(c_7,plain,
b != a,
inference(copy,[status(thm)],[c_6]) ).
fof(nnf_2,plain,
? [X] : ~ big_p(X),
inference(fof_nnf,[status(thm)],[pel49_neg]) ).
fof(sk_pel49_neg,plain,
~ big_p(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X,sK2)],[nnf_2]) ).
cnf(c_8,negated_conjecture,
~ big_p(sK2),
inference(split_conjunct,[status(thm)],[sk_pel49_neg]) ).
cnf(c_9,plain,
( A = B
| sK0 = B
| sK0 = A ),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_10,plain,
( big_p(sK1)
| sK0 = a ),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_11,plain,
( big_p(sK1)
| sK0 = b ),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_72,plain,
( ~ big_p(sK1)
| sK0 = sK2 ),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_14,plain,
( ~ big_p(sK1)
| sK2 = sK0 ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_16,plain,
( big_p(sK0)
| a = A
| sK0 = A ),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_34,plain,
( sK0 = b
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_35,plain,
( sK0 = a
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_43,plain,
( ~ big_p(sK0)
| sK0 = b ),
inference(paramod,[status(thm)],[c_34,c_8]) ).
cnf(c_53,plain,
( a = A
| sK0 = A
| sK0 = b ),
inference(resolve,[status(thm)],[c_43,c_16]) ).
cnf(c_73,plain,
( a = b
| sK0 = b ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_74,plain,
( b = a
| sK0 = b ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_56,plain,
sK0 = b,
inference(resolve,[status(thm)],[c_7,c_74]) ).
cnf(c_60,plain,
( ~ big_p(sK0)
| sK0 = a ),
inference(paramod,[status(thm)],[c_35,c_8]) ).
cnf(c_75,plain,
( ~ big_p(b)
| sK0 = a ),
inference(paramod,[status(thm)],[c_56,c_60]) ).
cnf(c_67,plain,
sK0 = a,
inference(resolve,[status(thm)],[c_5,c_75]) ).
cnf(c_76,plain,
a = b,
inference(paramod,[status(thm)],[c_67,c_56]) ).
cnf(c_77,plain,
b = a,
inference(copy,[status(thm)],[c_76]) ).
cnf(c_71,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN072+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 17:11:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 960062 was started by sandbox on n018,
% 0.10/0.37 % Sat Sep 26 17:11:36 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 21.
% 0.10/0.38 % Level of proof is 8.
% 0.10/0.38 % Maximum clause weight is 14.000.
% 0.10/0.38 % Given clauses 20.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------