%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE061+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 01:51:31 PM UTC 2026
% Result : Theorem 0.08s 5.91s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 4 sgn 32 !; 1 ?)
% 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(t15,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)],[t15]) ).
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/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(t21,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t38,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t21]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/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(t6,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t23,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t40,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t38,t23]) ).
cnf(t232,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t278,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t44,t232]) ).
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(t8,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(t10,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t49,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t264,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t8,t49]) ).
cnf(t69,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t264]) ).
cnf(t279,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t278,t69]) ).
cnf(t280,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t279,t23]) ).
cnf(t244,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t280]) ).
cnf(t245,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t244]) ).
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(t14,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t72,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t14]) ).
cnf(t74,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t72,t23]) ).
cnf(t266,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t74,t23]) ).
cnf(t102,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t266]) ).
cnf(t248,plain,
domain(X1) = multiplication(domain(X1),domain(X1)),
inference(cp,[status(thm)],[t245,t102]) ).
cnf(t258,plain,
multiplication(domain(X1),domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t248]) ).
fof(f17,conjecture,
! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),domain(X0)) = domain(X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0] : multiplication(domain(X0),domain(X0)) != domain(X0),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
multiplication(domain(sk0),domain(sk0)) != domain(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c18,plain,
multiplication(domain(sk0),domain(sk0)) != domain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(domain(sk0),domain(sk0)) != domain(sk0),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
domain(sk0) != domain(sk0),
inference(rw,[status(thm)],[goal_0,t258]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE061+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/5.31 % Computer : n012.cluster.edu
% 0.05/5.31 % Model : x86_64 x86_64
% 0.05/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.31 % Memory : 8046.5625MB
% 0.05/5.31 % OS : Linux 6.8.0-71-generic
% 0.05/5.31 % CPULimit : 300
% 0.05/5.31 % WCLimit : 300
% 0.05/5.31 % DateTime : Wed Sep 23 18:49:11 UTC 2026
% 0.05/5.31 % CPUTime :
% 0.05/5.31 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------