%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN403+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 : n026.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 5.76s 6.18s
% Output : Proof 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 43 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 6 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 9 ( 2 sgn 2 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X] :
( ( ( g(X)
=> h(X) )
& ( f(X)
=> g(X) ) )
=> ( f(X)
=> h(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish234) ).
fof(f0_neg,negated_conjecture,
~ ! [X] :
( ( ( g(X)
=> h(X) )
& ( f(X)
=> g(X) ) )
=> ( f(X)
=> h(X) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X] :
( ~ h(X)
& f(X)
& ( h(X)
| ~ g(X) )
& ( g(X)
| ~ f(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ~ h(sk0)
& f(sk0)
& ( h(sk0)
| ~ g(sk0) )
& ( g(sk0)
| ~ f(sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( h(sk0)
| ~ g(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
ifeq(g(sk0),true,h(sk0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c0,plain,
( g(sk0)
| ~ f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(f(sk0),true,g(sk0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c2,plain,
f(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
f(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1,plain,
g(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(t7,plain,
g(sk0) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t9,plain,
ifeq(true,true,h(sk0),true) = true,
inference(step,[status(thm)],[t5,t7]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t10,plain,
h(sk0) = true,
inference(step,[status(thm)],[t9,t6]) ).
cnf(t8,plain,
h(sk0) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(c3,plain,
~ h(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
h(sk0) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN403+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 01:08:15 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.76/6.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.76/6.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------