%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN406+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:34:37 PM UTC 2026
% Result : Theorem 0.16s 20.71s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 40 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 6 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 15 ( 0 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( f(X)
=> g(X) ) )
=> ? [Z] :
( h(Z)
& g(Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish240) ).
fof(f0_neg,negated_conjecture,
~ ( ( ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( f(X)
=> g(X) ) )
=> ? [Z] :
( h(Z)
& g(Z) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [Z] :
( ~ h(Z)
| ~ g(Z) )
& ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( g(X)
| ~ f(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z] :
( ( ~ h(Z)
| ~ g(Z) )
& h(sk0)
& f(sk0)
& ( g(X)
| ~ f(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c0,plain,
( g(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(f(X0),true,g(X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c1,plain,
f(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
f(sk0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
g(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1]) ).
cnf(c3,plain,
( ~ h(X2)
| ~ g(X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(g(X0),true,ifeq(h(X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c2,plain,
h(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
h(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi3,h0,hi2]) ).
cnf(t13,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN406+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.03/20.23 % CPULimit : 300
% 0.03/20.23 % WCLimit : 300
% 0.03/20.23 % DateTime : Fri Sep 25 01:05:27 UTC 2026
% 0.03/20.24 % CPUTime :
% 0.03/20.24 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/20.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/20.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------