%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE066+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 : n001.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 01:51:32 PM UTC 2026
% Result : Theorem 6.66s 1.33s
% Output : Proof 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t18,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t49,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t18]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t17,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t83,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t17]) ).
fof(f17,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
<= multiplication(X0,domain(X1)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
<= multiplication(X0,domain(X1)) = zero ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] :
( multiplication(X0,X1) != zero
& multiplication(X0,domain(X1)) = zero ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( multiplication(sk0,sk1) != zero
& multiplication(sk0,domain(sk1)) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
multiplication(sk0,domain(sk1)) = zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t12,plain,
multiplication(sk0,domain(sk1)) = zero,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t52,plain,
multiplication(sk0,domain(sk1)) = zero,
inference(orient,[status(thm)],[t12]) ).
cnf(t84,plain,
domain(multiplication(sk0,sk1)) = domain(zero),
inference(cp,[status(thm)],[t83,t52]) ).
fof(f15,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f15_nnf,plain,
domain(zero) = zero,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t0,plain,
domain(zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t81,plain,
domain(zero) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t132,plain,
domain(multiplication(sk0,sk1)) = zero,
inference(step,[status(thm)],[t84,t81]) ).
cnf(t117,plain,
domain(multiplication(sk0,sk1)) = zero,
inference(orient,[status(thm)],[t132]) ).
cnf(t120,plain,
multiplication(domain(multiplication(sk0,sk1)),multiplication(sk0,sk1)) = addition(multiplication(sk0,sk1),multiplication(zero,multiplication(sk0,sk1))),
inference(cp,[status(thm)],[t49,t117]) ).
cnf(t133,plain,
multiplication(zero,multiplication(sk0,sk1)) = addition(multiplication(sk0,sk1),multiplication(zero,multiplication(sk0,sk1))),
inference(step,[status(thm)],[t120,t117]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f10_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t9,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t47,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t9]) ).
cnf(t134,plain,
zero = addition(multiplication(sk0,sk1),multiplication(zero,multiplication(sk0,sk1))),
inference(step,[status(thm)],[t133,t47]) ).
cnf(t135,plain,
zero = addition(multiplication(sk0,sk1),zero),
inference(step,[status(thm)],[t134,t47]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t28,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t136,plain,
zero = multiplication(sk0,sk1),
inference(step,[status(thm)],[t135,t28]) ).
cnf(t123,plain,
multiplication(sk0,sk1) = zero,
inference(orient,[status(thm)],[t136]) ).
cnf(c19,plain,
multiplication(sk0,sk1) != zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(sk0,sk1) != zero,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t123]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE066+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 18:55:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.66/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.66/1.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------