%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE064+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 : n007.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 12:57:54 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 26 unt; 0 def)
% Number of atoms : 48 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 6 |; 4 &)
% ( 1 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 60 ( 58 !; 2 ?)
% 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(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,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(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)
<= addition(domain(X0),domain(X1)) = domain(X1) ),
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(f28,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
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(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
? [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
& addition(X0,multiplication(domain(X1),X0)) != multiplication(domain(X1),X0) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( addition(domain(sK0_skl),domain(sK1_skl)) = domain(sK1_skl)
& addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl)) != multiplication(domain(sK1_skl),sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40]) ).
fof(f42,plain,
addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl)) != multiplication(domain(sK1_skl),sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
addition(domain(sK0_skl),domain(sK1_skl)) = domain(sK1_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f48,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f55,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f156,plain,
domain(addition(sK0_skl,sK1_skl)) = domain(sK1_skl),
inference(backward_demodulation,[status(thm)],[f39,f43]) ).
fof(f157,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)),
inference(paramodulation,[status(thm)],[f20,f39]) ).
fof(f619,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f34,f55]) ).
fof(f807,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f48,f619]) ).
fof(f1129,plain,
! [X0,X1] : leq(X0,addition(X1,multiplication(domain(X0),X0))),
inference(paramodulation,[status(thm)],[f35,f807]) ).
fof(f2283,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,domain(X0)),X0)),
inference(paramodulation,[status(thm)],[f28,f1129]) ).
fof(f2956,plain,
! [X0,X1] : leq(X0,multiplication(domain(addition(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f157,f2283]) ).
fof(f3187,plain,
leq(sK0_skl,multiplication(domain(sK1_skl),sK0_skl)),
inference(paramodulation,[status(thm)],[f156,f2956]) ).
fof(f3402,plain,
addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl)) = multiplication(domain(sK1_skl),sK0_skl),
inference(resolution,[status(thm)],[f3187,f33]) ).
fof(f3403,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3402,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE064+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:39:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.52 % Elapsed time: 0.139397 seconds
% 0.39/0.52 % CPU time: 0.843828 seconds
% 0.39/0.52 % Total memory used: 80.679 MB
% 0.39/0.52 % Net memory used: 80.156 MB
%------------------------------------------------------------------------------