%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE070+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 : n003.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 4.07s 1.01s
% Output : Proof 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 53 ( 4 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t22,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t53,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t26,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t55,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t53,t26]) ).
cnf(t254,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t55]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/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/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(t12,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t32,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t266,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t32]) ).
cnf(t63,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t266]) ).
fof(f17,conjecture,
! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) != domain(X0),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
addition(domain(sk0),multiplication(domain(sk0),domain(sk1))) != domain(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
addition(domain(sk0),multiplication(domain(sk0),domain(sk1))) != domain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
addition(domain(sk0),multiplication(domain(sk0),domain(sk1))) != domain(sk0),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
multiplication(domain(sk0),addition(one,domain(sk1))) != domain(sk0),
inference(rw,[status(thm)],[goal_0,t254]) ).
cnf(g0_1,plain,
multiplication(domain(sk0),one) != domain(sk0),
inference(rw,[status(thm)],[g0_0,t63]) ).
cnf(g0_2,plain,
domain(sk0) != domain(sk0),
inference(rw,[status(thm)],[g0_1,t26]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE070+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:52:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.07/1.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.07/1.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------