%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN405+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 : n014.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 3.52s 0.81s
% Output : Proof 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 20 unt; 0 def)
% Number of atoms : 38 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 3 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 27 ( 9 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ? [Y] : g(Y)
& ! [X] : f(X) )
=> ? [Z] :
( g(Z)
& f(Z) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish239) ).
fof(f0_neg,negated_conjecture,
~ ( ( ? [Y] : g(Y)
& ! [X] : f(X) )
=> ? [Z] :
( g(Z)
& f(Z) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [Z] :
( ~ g(Z)
| ~ f(Z) )
& ? [Y] : g(Y)
& ! [X] : f(X) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z] :
( ( ~ g(Z)
| ~ f(Z) )
& g(sk0)
& f(X) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c2,plain,
( ~ g(X2)
| ~ f(X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
ifeq(f(X1),true,ifeq(g(X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t5,plain,
ifeq(f(X1),true,ifeq(g(X1),true,false,true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(c0,plain,
f(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
f(X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t6,plain,
f(X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t13,plain,
ifeq(true,true,ifeq(g(X1),true,false,true),true) = true,
inference(step,[status(thm)],[t5,t6]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t14,plain,
ifeq(g(X1),true,false,true) = true,
inference(step,[status(thm)],[t13,t4]) ).
cnf(t7,plain,
ifeq(g(X1),true,false,true) = true,
inference(rw,[status(thm)],[t14]) ).
cnf(t9,plain,
ifeq(g(X1),true,false,true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(c1,plain,
g(sk0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
g(sk0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
g(sk0) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t10,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t9,t8]) ).
cnf(t15,plain,
true = false,
inference(step,[status(thm)],[t10,t4]) ).
cnf(t11,plain,
false = true,
inference(orient,[status(thm)],[t15]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN405+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 01:05:18 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.52/0.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.52/0.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------