%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE009+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 : n017.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 52.29s 13.08s
% Output : Proof 52.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 105 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 98 ( 41 ~; 31 |; 20 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 49 !; 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(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(p31,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(p212,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(superposition,[status(thm)],[c0,p31]) ).
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]) ).
fof(f16,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
( ( ~ leq(addition(addition(addition(multiplication(sk1,sk2),multiplication(sk1,c(sk2))),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2))),one)
| ~ leq(one,addition(addition(addition(multiplication(sk1,sk2),multiplication(sk1,c(sk2))),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2)))) )
& test(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(p150,plain,
( complement(sk2,X0)
| c(sk2) != X0 ),
inference(resolution,[status(thm)],[c19,c22]) ).
cnf(p152,plain,
complement(sk2,c(sk2)),
inference(equality_resolution,[status(thm)],[p150]) ).
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(p156,plain,
addition(sk2,c(sk2)) = one,
inference(resolution,[status(thm)],[p152,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(p55,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[status(thm)],[c7,c0]) ).
cnf(c24,plain,
( ~ leq(addition(addition(addition(multiplication(sk1,sk2),multiplication(sk1,c(sk2))),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2))),one)
| ~ leq(one,addition(addition(addition(multiplication(sk1,sk2),multiplication(sk1,c(sk2))),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2)))) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p57,plain,
( ~ leq(addition(addition(multiplication(sk1,addition(c(sk2),sk2)),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2))),one)
| ~ leq(one,addition(addition(multiplication(sk1,addition(c(sk2),sk2)),multiplication(c(sk1),sk2)),multiplication(c(sk1),c(sk2)))) ),
inference(demodulation,[status(thm)],[p55,c24]) ).
cnf(p63,plain,
( ~ leq(addition(multiplication(c(sk1),c(sk2)),addition(multiplication(c(sk1),sk2),multiplication(sk1,addition(sk2,c(sk2))))),one)
| ~ leq(one,addition(multiplication(c(sk1),c(sk2)),addition(multiplication(c(sk1),sk2),multiplication(sk1,addition(sk2,c(sk2)))))) ),
inference(superposition,[status(thm)],[c0,p57]) ).
cnf(p158,plain,
( ~ leq(addition(multiplication(c(sk1),c(sk2)),addition(multiplication(c(sk1),sk2),multiplication(sk1,one))),one)
| ~ leq(one,addition(multiplication(c(sk1),c(sk2)),addition(multiplication(c(sk1),sk2),multiplication(sk1,one)))) ),
inference(demodulation,[status(thm)],[p156,p63]) ).
cnf(p217,plain,
( ~ leq(addition(multiplication(sk1,one),addition(multiplication(c(sk1),sk2),multiplication(c(sk1),c(sk2)))),one)
| ~ leq(one,addition(multiplication(sk1,one),addition(multiplication(c(sk1),sk2),multiplication(c(sk1),c(sk2))))) ),
inference(demodulation,[status(thm)],[p212,p158]) ).
cnf(p1126,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(superposition,[status(thm)],[c0,p217]) ).
cnf(p1137,plain,
~ leq(one,one),
inference(factoring,[status(thm)],[p1126]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
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]) ).
cnf(p90,plain,
leq(X0,X0),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(p1138,plain,
$false,
inference(resolution,[status(thm)],[p1137,p90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.39 % Computer : n017.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Wed Sep 23 18:30:51 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 52.29/13.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.29/13.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------