%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN402+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 : n012.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 2.84s 0.74s
% Output : Proof 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 22 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 3 sgn 4 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X] :
( f(X)
=> ? [Y] : f(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish230) ).
fof(f0_neg,negated_conjecture,
~ ! [X] :
( f(X)
=> ? [Y] : f(Y) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X] :
( ! [Y] : ~ f(Y)
& f(X) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y] :
( ~ f(Y)
& f(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
~ f(X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
eq(f(X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t5,plain,
eq(f(X1),true) = efalse,
inference(orient,[status(thm)],[t2]) ).
cnf(c0,plain,
f(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
f(sk0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t3,plain,
f(sk0) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t6,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t5,t3]) ).
cnf(t1,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t4,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t1]) ).
cnf(t10,plain,
efalse = etrue,
inference(step,[status(thm)],[t6,t4]) ).
cnf(t7,plain,
efalse = etrue,
inference(orient,[status(thm)],[t10]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t7]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN402+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Fri Sep 25 01:04:51 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.84/0.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/0.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------