%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE007+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 : n010.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 01:51:19 PM UTC 2026
% Result : Theorem 37.54s 6.78s
% Output : Proof 37.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 17 unt; 0 def)
% Number of atoms : 69 ( 40 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 64 ( 25 ~; 18 |; 16 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 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 : 46 ( 0 sgn 31 !; 2 ?)
% 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(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(p109,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
fof(f18,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,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(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
? [X0,X1] :
( one != addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))
& test(X0)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( one != addition(multiplication(addition(sk1,c(sk1)),sk2),multiplication(addition(sk1,c(sk1)),c(sk2)))
& test(sk1)
& test(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f18_nnf]) ).
cnf(c25,plain,
test(sk1),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p113,plain,
complement(sk1,c(sk1)),
inference(resolution,[status(thm)],[p109,c25]) ).
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(p124,plain,
addition(sk1,c(sk1)) = one,
inference(resolution,[status(thm)],[p113,c17]) ).
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(p42,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(c26,plain,
one != addition(multiplication(addition(sk1,c(sk1)),sk2),multiplication(addition(sk1,c(sk1)),c(sk2))),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p44,plain,
one != multiplication(addition(sk1,c(sk1)),addition(c(sk2),sk2)),
inference(demodulation,[status(thm)],[p42,c26]) ).
cnf(p125,plain,
one != multiplication(one,addition(c(sk2),sk2)),
inference(demodulation,[status(thm)],[p124,p44]) ).
cnf(p188,plain,
one != one,
inference(superposition,[status(thm)],[c0,p125]) ).
cnf(p195,plain,
$false,
inference(equality_resolution,[status(thm)],[p188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE007+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n010.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 18:34:13 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 37.54/6.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.54/6.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------