%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE021+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 : n019.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 01:51:23 PM UTC 2026
% Result : Theorem 22.71s 8.55s
% Output : Proof 22.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 22 unt; 0 def)
% Number of atoms : 70 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 61 ( 26 ~; 18 |; 12 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
fof(f14,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f14_nnf,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p103,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
fof(f16,conjecture,
! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1] :
( X0 != addition(multiplication(X1,X0),multiplication(c(X1),X0))
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( sk1 != addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1))
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f16_nnf]) ).
cnf(c22,plain,
test(sk2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p106,plain,
complement(sk2,c(sk2)),
inference(resolution,[status(thm)],[p103,c22]) ).
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]) ).
cnf(p110,plain,
addition(sk2,c(sk2)) = one,
inference(resolution,[status(thm)],[p106,c17]) ).
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(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(p50,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X2,X0),X1),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(c23,plain,
sk1 != addition(multiplication(sk2,sk1),multiplication(c(sk2),sk1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p52,plain,
sk1 != multiplication(addition(c(sk2),sk2),sk1),
inference(demodulation,[status(thm)],[p50,c23]) ).
cnf(p55,plain,
sk1 != multiplication(addition(sk2,c(sk2)),sk1),
inference(superposition,[status(thm)],[c0,p52]) ).
cnf(p111,plain,
sk1 != multiplication(one,sk1),
inference(demodulation,[status(thm)],[p110,p55]) ).
cnf(p117,plain,
sk1 != sk1,
inference(superposition,[status(thm)],[c6,p111]) ).
cnf(p118,plain,
$false,
inference(equality_resolution,[status(thm)],[p117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE021+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/5.60 % Computer : n019.cluster.edu
% 0.02/5.60 % Model : x86_64 x86_64
% 0.02/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/5.60 % Memory : 8046.5625MB
% 0.02/5.60 % OS : Linux 6.8.0-71-generic
% 0.02/5.60 % CPULimit : 300
% 0.02/5.60 % WCLimit : 300
% 0.02/5.60 % DateTime : Wed Sep 23 18:38:58 UTC 2026
% 0.02/5.60 % CPUTime :
% 0.02/5.60 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.71/8.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.71/8.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------