%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 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 01:51:31 PM UTC 2026
% Result : Theorem 26.04s 3.84s
% Output : Proof 26.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 68 unt; 0 def)
% Number of atoms : 76 ( 75 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 7 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/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(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f8_nnf,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t24,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t41,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t24]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t43,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t41,t26]) ).
cnf(t278,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t43]) ).
cnf(t19781,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t49,t278]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t11,plain,
addition(domain(X1),one) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/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(t13,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t58,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t19764,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t11,t58]) ).
cnf(t78,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t19764]) ).
cnf(t19782,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t19781,t78]) ).
cnf(t19783,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t19782,t26]) ).
cnf(t296,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t19783]) ).
cnf(t297,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t296]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/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]) ).
cnf(t301,plain,
multiplication(X1,domain(X2)) = multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2))),
inference(cp,[status(thm)],[t297,t83]) ).
cnf(t19571,plain,
multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2))) = multiplication(X1,domain(X2)),
inference(orient,[status(thm)],[t301]) ).
fof(f17,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
file('/export/starexec/sandbox/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,domain(X1)) != zero
& multiplication(X0,X1) = zero ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( multiplication(sk0,domain(sk1)) != zero
& multiplication(sk0,sk1) = zero ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
multiplication(sk0,sk1) = zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t9,plain,
multiplication(sk0,sk1) = zero,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t52,plain,
multiplication(sk0,sk1) = zero,
inference(orient,[status(thm)],[t9]) ).
cnf(t19644,plain,
multiplication(sk0,domain(sk1)) = multiplication(domain(zero),multiplication(sk0,domain(sk1))),
inference(cp,[status(thm)],[t19571,t52]) ).
fof(f15,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/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(t20025,plain,
multiplication(sk0,domain(sk1)) = multiplication(zero,multiplication(sk0,domain(sk1))),
inference(step,[status(thm)],[t19644,t81]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/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(t10,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t47,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t10]) ).
cnf(t20026,plain,
multiplication(sk0,domain(sk1)) = zero,
inference(step,[status(thm)],[t20025,t47]) ).
cnf(t19737,plain,
multiplication(sk0,domain(sk1)) = zero,
inference(orient,[status(thm)],[t20026]) ).
cnf(c19,plain,
multiplication(sk0,domain(sk1)) != zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(sk0,domain(sk1)) != zero,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t19737]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 % Computer : n006.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Wed Sep 23 18:49:27 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.04/3.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.04/3.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------