%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN080+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 : n006.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 03:33:45 PM UTC 2026
% Result : Theorem 5.49s 1.13s
% Output : Proof 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X,Y] : f(f(X)) = f(g(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel58) ).
fof(f1_neg,negated_conjecture,
~ ! [X,Y] : f(f(X)) = f(g(Y)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [X,Y] : f(f(X)) != f(g(Y)),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
f(f(sk0)) != f(g(sk1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f1_nnf]) ).
cnf(c1,plain,
f(f(sk0)) != f(g(sk1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
f(g(sk1)) != f(f(sk0)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
g(sk1) != f(f(sk0)),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
g(sk1) != g(sk1),
inference(rw,[status(thm)],[g0_0]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN080+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 00:06:55 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.49/1.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.49/1.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------