%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN920+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:43:22 AM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 6 unt; 0 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 168 ( 59 ~; 63 |; 32 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X0] :
( ~ h(X0)
& g(X0)
& f(X0) ) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ( ~ g(sK1)
& f(sK1) )
| ( ~ h(sK0)
& g(sK0)
& f(sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X,sK1)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ! [VAR_0] :
( h(VAR_0)
| ~ g(VAR_0)
| ~ f(VAR_0) )
& ! [VAR_0] :
( g(VAR_0)
| ~ h(VAR_0)
| ~ f(VAR_0) )
& ! [VAR_0,VAR_1] :
( h(VAR_1)
| ~ f(VAR_1)
| g(VAR_0)
| ~ f(VAR_0) )
& ( ~ g(sK1)
| ~ h(sK0) )
& ( f(sK1)
| ~ h(sK0) )
& ( ~ g(sK1)
| g(sK0) )
& ( f(sK1)
| g(sK0) )
& ( ~ g(sK1)
| f(sK0) )
& ( f(sK1)
| f(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( h(B)
| ~ f(B)
| g(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( ~ g(sK1)
| ~ h(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( f(sK1)
| ~ h(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( g(A)
| ~ h(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( h(A)
| ~ g(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
( f(sK1)
| ~ g(sK0)
| ~ f(sK0) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_8,negated_conjecture,
( ~ g(sK1)
| ~ g(sK0)
| ~ f(sK0) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_9,negated_conjecture,
( ~ f(A)
| g(B)
| ~ f(B)
| g(A)
| ~ f(A) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_10,negated_conjecture,
( g(B)
| ~ f(B)
| g(A)
| ~ f(A) ),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_14,negated_conjecture,
( f(sK1)
| g(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_15,negated_conjecture,
( ~ g(sK1)
| f(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_16,negated_conjecture,
( f(sK1)
| f(sK0) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_26,plain,
( g(A)
| g(A)
| ~ f(A) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_17,plain,
( g(A)
| ~ f(A) ),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_27,negated_conjecture,
( f(sK1)
| ~ f(sK0)
| f(sK1) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_18,negated_conjecture,
( ~ f(sK0)
| f(sK1) ),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_19,plain,
( f(sK0)
| g(sK1) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_28,negated_conjecture,
( f(sK0)
| f(sK0) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_20,negated_conjecture,
f(sK0),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_21,negated_conjecture,
f(sK1),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_22,negated_conjecture,
( ~ g(sK1)
| ~ g(sK0) ),
inference(resolve,[status(thm)],[c_20,c_8]) ).
cnf(c_23,plain,
g(sK0),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_24,negated_conjecture,
~ g(sK1),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_29,plain,
g(sK1),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_25,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN920+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 18:55:01 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 1491153 was started by sandbox on n016,
% 0.09/0.36 % Sat Sep 26 18:55:01 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 22.
% 0.09/0.37 % Level of proof is 9.
% 0.09/0.37 % Maximum clause weight is 8.000.
% 0.09/0.37 % Given clauses 11.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------