%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:51:30 PM UTC 2026
% Result : Theorem 3.51s 0.83s
% Output : Proof 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 0-2 aty)
% Number of variables : 30 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f16_nnf,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t17,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t61,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t17]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t14,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t34,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
fof(f17,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] :
( addition(domain(X0),domain(X1)) != domain(X1)
& addition(X0,X1) = X1 ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( addition(domain(sk0),domain(sk1)) != domain(sk1)
& addition(sk0,sk1) = sk1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
addition(sk0,sk1) = sk1,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t3,plain,
addition(sk0,sk1) = sk1,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t72,plain,
addition(sk1,sk0) = sk1,
inference(step,[status(thm)],[t3,t34]) ).
cnf(t68,plain,
addition(sk1,sk0) = sk1,
inference(orient,[status(thm)],[t72]) ).
cnf(c19,plain,
addition(domain(sk0),domain(sk1)) != domain(sk1),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
addition(domain(sk0),domain(sk1)) != domain(sk1),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
domain(addition(sk0,sk1)) != domain(sk1),
inference(rw,[status(thm)],[goal_0,t61]) ).
cnf(g0_1,plain,
domain(addition(sk1,sk0)) != domain(sk1),
inference(rw,[status(thm)],[g0_0,t34]) ).
cnf(g0_2,plain,
domain(sk1) != domain(sk1),
inference(rw,[status(thm)],[g0_1,t68]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 18:48:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.51/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.51/0.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------