%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN918+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 : n017.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 156 ( 54 ~; 56 |; 32 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 53 ( 3 sgn 28 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [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) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [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] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
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) ) )
& ! [X] :
( ( ~ g(sK0(X))
& f(sK0(X)) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[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) )
& ! [VAR_0] :
( ~ g(sK0(VAR_0))
| ~ h(VAR_0) )
& ! [VAR_0] :
( f(sK0(VAR_0))
| ~ h(VAR_0) )
& ! [VAR_0] :
( ~ g(sK0(VAR_0))
| g(VAR_0) )
& ! [VAR_0] :
( f(sK0(VAR_0))
| g(VAR_0) )
& ! [VAR_0] :
( ~ g(sK0(VAR_0))
| f(VAR_0) )
& ! [VAR_0] :
( f(sK0(VAR_0))
| f(VAR_0) ) ),
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(sK0(A))
| ~ h(A) ),
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_8,negated_conjecture,
( ~ g(sK0(A))
| ~ g(A)
| ~ f(A) ),
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_15,negated_conjecture,
( ~ g(sK0(A))
| f(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_16,negated_conjecture,
( f(sK0(A))
| f(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_29,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_29]) ).
cnf(c_22,plain,
( f(A)
| g(sK0(A)) ),
inference(resolve,[status(thm)],[c_17,c_16]) ).
cnf(c_30,negated_conjecture,
( f(A)
| f(A) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_26,negated_conjecture,
f(A),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_27,plain,
g(A),
inference(resolve,[status(thm)],[c_26,c_17]) ).
cnf(c_31,negated_conjecture,
( ~ g(sK0(A))
| ~ g(A) ),
inference(resolve,[status(thm)],[c_26,c_8]) ).
cnf(c_32,negated_conjecture,
~ g(sK0(A)),
inference(resolve,[status(thm)],[c_27,c_31]) ).
cnf(c_28,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_27,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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 18:45:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1417063 was started by sandbox on n017,
% 0.08/0.36 % Sat Sep 26 18:45:18 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 15.
% 0.13/0.37 % Level of proof is 8.
% 0.13/0.37 % Maximum clause weight is 8.000.
% 0.13/0.37 % Given clauses 10.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------