%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Thu Sep 24 12:57:52 PM UTC 2026
% Result : Theorem 0.22s 10.82s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 28 unt; 0 def)
% Number of atoms : 50 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 6 |; 4 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
? [X0] :
( addition(X0,domain(X0)) != domain(X0)
& addition(X0,one) = one ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( addition(sK0_skl,domain(sK0_skl)) != domain(sK0_skl)
& addition(sK0_skl,one) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
addition(sK0_skl,one) = one,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
addition(sK0_skl,domain(sK0_skl)) != domain(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f71,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f80,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f144,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f428,plain,
~ leq(sK0_skl,domain(sK0_skl)),
inference(resolution,[status(thm)],[f43,f33]) ).
fof(f594,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f23,f71]) ).
fof(f635,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f80,f34]) ).
fof(f699,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f71,f635]) ).
fof(f766,plain,
! [X0,X1] : leq(X0,addition(X1,multiplication(domain(X0),X0))),
inference(paramodulation,[status(thm)],[f35,f699]) ).
fof(f1165,plain,
addition(sK0_skl,one) = addition(one,sK0_skl),
inference(paramodulation,[status(thm)],[f42,f594]) ).
fof(f1218,plain,
one = addition(one,sK0_skl),
inference(forward_demodulation,[status(thm)],[f42,f1165]) ).
fof(f2247,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK0_skl)),
inference(paramodulation,[status(thm)],[f1218,f144]) ).
fof(f2303,plain,
! [X0] : X0 = addition(X0,multiplication(X0,sK0_skl)),
inference(forward_demodulation,[status(thm)],[f25,f2247]) ).
fof(f3843,plain,
leq(sK0_skl,domain(sK0_skl)),
inference(paramodulation,[status(thm)],[f2303,f766]) ).
fof(f3858,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3843,f428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.68 % Computer : n001.cluster.edu
% 0.17/10.68 % Model : x86_64 x86_64
% 0.17/10.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.68 % Memory : 8046.5625MB
% 0.17/10.68 % OS : Linux 6.8.0-71-generic
% 0.17/10.68 % CPULimit : 300
% 0.17/10.68 % WCLimit : 300
% 0.17/10.68 % DateTime : Sun Sep 20 22:47:08 UTC 2026
% 0.17/10.68 % CPUTime :
% 0.22/10.70 % Drodi V4.1.1
% 0.22/10.82 % Refutation found
% 0.22/10.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/10.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/10.88 % Elapsed time: 0.182778 seconds
% 0.22/10.88 % CPU time: 0.998087 seconds
% 0.22/10.88 % Total memory used: 77.773 MB
% 0.22/10.88 % Net memory used: 77.296 MB
%------------------------------------------------------------------------------