%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE064+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 : n011.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 6.41s 6.28s
% Output : Proof 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 65 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 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 : 90 ( 7 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t25,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t49,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t25]) ).
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(t29,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t51,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t29]) ).
cnf(t238,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t51]) ).
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(t10,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(t12,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)],[t12]) ).
cnf(t625,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t34]) ).
cnf(t65,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t625]) ).
fof(f17,conjecture,
! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) != multiplication(domain(X1),X0)
& addition(domain(X0),domain(X1)) = domain(X1) ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( addition(sk0,multiplication(domain(sk1),sk0)) != multiplication(domain(sk1),sk0)
& addition(domain(sk0),domain(sk1)) = domain(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
addition(domain(sk0),domain(sk1)) = domain(sk1),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t15,plain,
addition(domain(sk0),domain(sk1)) = domain(sk1),
inference(equality_encoding,[status(esa)],[c18]) ).
fof(f16,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/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]) ).
cnf(t626,plain,
domain(addition(sk0,sk1)) = domain(sk1),
inference(step,[status(thm)],[t15,t61]) ).
cnf(t627,plain,
domain(addition(sk1,sk0)) = domain(sk1),
inference(step,[status(thm)],[t626,t34]) ).
cnf(t68,plain,
domain(addition(sk1,sk0)) = domain(sk1),
inference(orient,[status(thm)],[t627]) ).
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(t19,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t44,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t19]) ).
cnf(t641,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t44,t238]) ).
cnf(t642,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t641,t65]) ).
cnf(t643,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t642,t29]) ).
cnf(t249,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t643]) ).
cnf(t250,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t249]) ).
cnf(t261,plain,
multiplication(addition(domain(X1),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(cp,[status(thm)],[t49,t250]) ).
cnf(t657,plain,
multiplication(addition(domain(X1),X2),X1) = multiplication(addition(one,X2),X1),
inference(step,[status(thm)],[t261,t238]) ).
cnf(t586,plain,
multiplication(addition(domain(X1),X2),X1) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t657]) ).
cnf(t587,plain,
multiplication(addition(one,domain(X1)),X2) = multiplication(domain(addition(X2,X1)),X2),
inference(cp,[status(thm)],[t586,t61]) ).
cnf(t658,plain,
multiplication(one,X2) = multiplication(domain(addition(X2,X1)),X2),
inference(step,[status(thm)],[t587,t65]) ).
cnf(t659,plain,
X2 = multiplication(domain(addition(X2,X1)),X2),
inference(step,[status(thm)],[t658,t29]) ).
cnf(t611,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(orient,[status(thm)],[t659]) ).
cnf(c19,plain,
addition(sk0,multiplication(domain(sk1),sk0)) != multiplication(domain(sk1),sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
addition(sk0,multiplication(domain(sk1),sk0)) != multiplication(domain(sk1),sk0),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
multiplication(addition(one,domain(sk1)),sk0) != multiplication(domain(sk1),sk0),
inference(rw,[status(thm)],[goal_0,t238]) ).
cnf(g0_1,plain,
multiplication(one,sk0) != multiplication(domain(sk1),sk0),
inference(rw,[status(thm)],[g0_0,t65]) ).
cnf(g0_2,plain,
sk0 != multiplication(domain(sk1),sk0),
inference(rw,[status(thm)],[g0_1,t29]) ).
cnf(g0_3,plain,
sk0 != multiplication(domain(addition(sk1,sk0)),sk0),
inference(rw,[status(thm)],[g0_2,t68]) ).
cnf(g0_4,plain,
sk0 != multiplication(domain(addition(sk0,sk1)),sk0),
inference(rw,[status(thm)],[g0_3,t34]) ).
cnf(g0_5,plain,
sk0 != sk0,
inference(rw,[status(thm)],[g0_4,t611]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE064+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n011.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 18:50:03 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.41/6.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.41/6.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------