%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN070+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 : n011.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 138 ( 52 ~; 63 |; 16 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 8 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel46_1,axiom,
! [X,Y] :
( ( ( ( big_h(Y,X)
& big_f(Y) )
=> big_g(Y) )
& big_f(X) )
=> big_g(X) ),
file('theBenchmark.p',pel46_1) ).
fof(pel46_2,axiom,
( ? [X] :
( ~ big_g(X)
& big_f(X) )
=> ? [X1] :
( ! [Y] :
( ( ~ big_g(Y)
& big_f(Y) )
=> big_j(X1,Y) )
& ~ big_g(X1)
& big_f(X1) ) ),
file('theBenchmark.p',pel46_2) ).
fof(pel46_3,axiom,
! [X,Y] :
( ( big_h(X,Y)
& big_f(Y)
& big_f(X) )
=> ~ big_j(Y,X) ),
file('theBenchmark.p',pel46_3) ).
fof(pel46,conjecture,
! [X] :
( big_f(X)
=> big_g(X) ),
file('theBenchmark.p',pel46) ).
fof(pel46_neg,negated_conjecture,
~ ! [X] :
( big_f(X)
=> big_g(X) ),
inference(assume_negation,[status(cth)],[pel46]) ).
cnf(c_5,plain,
( ~ big_j(B,A)
| ~ big_h(A,B)
| ~ big_f(B)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel46_3]) ).
cnf(c_6,plain,
( big_g(A)
| big_h(B,A)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel46_1]) ).
fof(nnf_2,plain,
( ? [X1] :
( ! [Y] :
( big_j(X1,Y)
| big_g(Y)
| ~ big_f(Y) )
& ~ big_g(X1)
& big_f(X1) )
| ! [X] :
( big_g(X)
| ~ big_f(X) ) ),
inference(fof_nnf,[status(thm)],[pel46_2]) ).
fof(sk_pel46_2_sk,plain,
( ( ! [Y] :
( big_j(sK0,Y)
| big_g(Y)
| ~ big_f(Y) )
& ~ big_g(sK0)
& big_f(sK0) )
| ! [X] :
( big_g(X)
| ~ big_f(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[nnf_2]) ).
fof(sk_pel46_2,plain,
( ! [VAR_0,VAR_1] :
( big_j(sK0,VAR_1)
| big_g(VAR_1)
| ~ big_f(VAR_1)
| big_g(VAR_0)
| ~ big_f(VAR_0) )
& ! [VAR_0] :
( ~ big_g(sK0)
| big_g(VAR_0)
| ~ big_f(VAR_0) )
& ! [VAR_0] :
( big_f(sK0)
| big_g(VAR_0)
| ~ big_f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel46_2_sk]) ).
cnf(c_7,plain,
( big_j(sK0,B)
| big_g(B)
| ~ big_f(B)
| big_g(A)
| ~ big_f(A) ),
inference(split_conjunct,[status(thm)],[sk_pel46_2]) ).
cnf(c_8,plain,
( big_g(B)
| ~ big_f(B)
| ~ big_j(B,A)
| ~ big_f(B)
| ~ big_f(A) ),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,plain,
( big_g(sK0)
| ~ big_f(sK0)
| ~ big_f(sK0)
| ~ big_f(B)
| big_g(B)
| ~ big_f(B)
| big_g(A)
| ~ big_f(A) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_22,plain,
( big_g(sK0)
| ~ big_f(sK0)
| ~ big_f(sK0)
| big_g(B)
| ~ big_f(B)
| big_g(A)
| ~ big_f(A) ),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_10,plain,
( big_g(sK0)
| ~ big_f(sK0)
| big_g(B)
| ~ big_f(B)
| big_g(A)
| ~ big_f(A) ),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_11,plain,
( big_g(A)
| big_f(B)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel46_1]) ).
cnf(c_12,plain,
( big_g(A)
| ~ big_g(B)
| ~ big_f(A) ),
inference(clausify,[status(thm)],[pel46_1]) ).
fof(nnf_4,plain,
? [X] :
( ~ big_g(X)
& big_f(X) ),
inference(fof_nnf,[status(thm)],[pel46_neg]) ).
fof(sk_pel46_neg,plain,
( ~ big_g(sK1)
& big_f(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1)],[nnf_4]) ).
cnf(c_13,negated_conjecture,
big_f(sK1),
inference(split_conjunct,[status(thm)],[sk_pel46_neg]) ).
cnf(c_14,negated_conjecture,
~ big_g(sK1),
inference(split_conjunct,[status(thm)],[sk_pel46_neg]) ).
cnf(c_23,plain,
( big_g(sK0)
| ~ big_f(sK0)
| big_g(A)
| big_g(A)
| ~ big_f(A) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_15,plain,
( big_g(sK0)
| ~ big_f(sK0)
| big_g(A)
| ~ big_f(A) ),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_24,plain,
( big_g(sK0)
| big_g(sK0)
| ~ big_f(sK0) ),
inference(factor,[status(thm)],[c_15]) ).
cnf(c_16,plain,
( big_g(sK0)
| ~ big_f(sK0) ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_25,negated_conjecture,
( big_g(sK1)
| big_f(A) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_17,negated_conjecture,
big_f(A),
inference(resolve,[status(thm)],[c_14,c_25]) ).
cnf(c_18,plain,
big_g(sK0),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_19,plain,
( big_g(B)
| ~ big_g(A) ),
inference(resolve,[status(thm)],[c_17,c_12]) ).
cnf(c_20,plain,
big_g(A),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_21,plain,
$false,
inference(resolve,[status(thm)],[c_20,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN070+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:09:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1118207 was started by sandbox on n011,
% 0.09/0.36 % Sat Sep 26 17:09:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 21.
% 0.14/0.38 % Level of proof is 9.
% 0.14/0.38 % Maximum clause weight is 12.000.
% 0.14/0.38 % Given clauses 7.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------