%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE010+3 : 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 01:51:20 PM UTC 2026
% Result : Theorem 67.54s 10.38s
% Output : Proof 67.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 41 unt; 0 def)
% Number of atoms : 87 ( 58 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 61 ( 27 ~; 14 |; 16 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 51 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f13,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f13_nnf,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X0] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c17,plain,
( addition(X0,X1) = one
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f12,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
fof(f12_nnf,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( complement(sk0(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f12_nnf]) ).
cnf(c13,plain,
( complement(sk0(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f18,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( one != addition(addition(addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),multiplication(sk1,sk2)),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2)))
& test(sk1)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f18_nnf]) ).
cnf(c24,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p110,plain,
complement(sk0(sk2),sk2),
inference(resolution,[status(thm)],[c13,c24]) ).
cnf(p133,plain,
addition(sk2,sk0(sk2)) = one,
inference(resolution,[status(thm)],[c17,p110]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p34,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(p309,plain,
addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(superposition,[status(thm)],[c3,p34]) ).
cnf(p1728,plain,
addition(one,sk2) = one,
inference(superposition,[status(thm)],[p133,p309]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/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(p71,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(p1764,plain,
addition(X0,multiplication(X0,sk2)) = X0,
inference(superposition,[status(thm)],[p1728,p71]) ).
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(p84,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X2,X0),X1),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(p41,plain,
addition(addition(X0,X1),X2) = addition(addition(X2,X0),X1),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(c26,plain,
one != addition(addition(addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),multiplication(sk1,sk2)),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2))),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p30,plain,
one != addition(addition(multiplication(c(sk1),sk2),multiplication(c(sk1),c(sk2))),addition(multiplication(sk1,sk2),addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)))),
inference(superposition,[status(thm)],[c1,c26]) ).
cnf(p35,plain,
one != addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),addition(addition(multiplication(c(sk1),sk2),multiplication(c(sk1),c(sk2))),multiplication(sk1,sk2))),
inference(demodulation,[status(thm)],[p34,p30]) ).
cnf(p43,plain,
one != addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),addition(addition(multiplication(sk1,sk2),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2)))),
inference(demodulation,[status(thm)],[p41,p35]) ).
cnf(p59,plain,
one != addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),addition(multiplication(sk1,sk2),addition(multiplication(c(sk1),sk2),multiplication(c(sk1),c(sk2))))),
inference(superposition,[status(thm)],[c1,p43]) ).
cnf(p74,plain,
one != addition(addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),addition(multiplication(sk1,sk2),multiplication(c(sk1),addition(c(sk2),sk2)))),
inference(demodulation,[status(thm)],[p71,p59]) ).
cnf(p94,plain,
one != addition(multiplication(addition(c(sk2),sk2),sk1),addition(multiplication(sk1,sk2),multiplication(c(sk1),addition(c(sk2),sk2)))),
inference(demodulation,[status(thm)],[p84,p74]) ).
cnf(p311,plain,
one != addition(c(sk1),addition(sk1,multiplication(sk1,sk2))),
inference(superposition,[status(thm)],[p34,p94]) ).
cnf(p1765,plain,
one != addition(c(sk1),sk1),
inference(demodulation,[status(thm)],[p1764,p311]) ).
cnf(p1802,plain,
one != one,
inference(superposition,[status(thm)],[c0,p1765]) ).
cnf(p1803,plain,
$false,
inference(equality_resolution,[status(thm)],[p1802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.56 % Computer : n011.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Wed Sep 23 18:35:14 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.56 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 67.54/10.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.54/10.38 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------