%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:58:03 PM UTC 2026
% Result : Theorem 0.23s 1.15s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 41 unt; 0 def)
% Number of atoms : 89 ( 53 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 39 ~; 20 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 89 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0] :
( leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
& leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
& leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
? [X0] :
( ~ leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
| ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0)))
| ? [X0] : ~ leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ leq(strong_iteration(sK1_skl),multiplication(strong_iteration(sK1_skl),strong_iteration(sK1_skl)))
| ~ leq(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46]) ).
fof(f48,plain,
( ~ leq(strong_iteration(sK1_skl),multiplication(strong_iteration(sK1_skl),strong_iteration(sK1_skl)))
| ~ leq(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
( ~ leq(strong_iteration(sK1_skl),multiplication(strong_iteration(sK1_skl),strong_iteration(sK1_skl)))
| addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl) ),
inference(resolution,[status(thm)],[f44,f48]) ).
fof(f53,plain,
( ~ leq(strong_iteration(sK1_skl),addition(multiplication(sK1_skl,strong_iteration(sK1_skl)),strong_iteration(sK1_skl)))
| addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl) ),
inference(resolution,[status(thm)],[f52,f39]) ).
fof(f55,plain,
( addition(strong_iteration(sK1_skl),addition(multiplication(sK1_skl,strong_iteration(sK1_skl)),strong_iteration(sK1_skl))) != addition(multiplication(sK1_skl,strong_iteration(sK1_skl)),strong_iteration(sK1_skl))
| addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl) ),
inference(resolution,[status(thm)],[f53,f44]) ).
fof(f64,plain,
! [X0,X1] :
( leq(X0,strong_iteration(X1))
| ~ leq(X0,addition(multiplication(X1,X0),one)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f73,plain,
( addition(strong_iteration(sK1_skl),addition(strong_iteration(sK1_skl),multiplication(sK1_skl,strong_iteration(sK1_skl)))) != addition(multiplication(sK1_skl,strong_iteration(sK1_skl)),strong_iteration(sK1_skl))
| addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl) ),
inference(paramodulation,[status(thm)],[f21,f55]) ).
fof(f90,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f95,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) = X2
| ~ leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f22,f43]) ).
fof(f100,plain,
( addition(strong_iteration(sK1_skl),multiplication(sK1_skl,strong_iteration(sK1_skl))) != addition(multiplication(sK1_skl,strong_iteration(sK1_skl)),strong_iteration(sK1_skl))
| addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f90,f73]) ).
fof(f101,plain,
addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != strong_iteration(sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f100,f21]) ).
fof(f114,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f28,f22]) ).
fof(f138,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f192,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f24,f95]) ).
fof(f275,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f90]) ).
fof(f381,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f21,f37]) ).
fof(f386,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f37,f275]) ).
fof(f396,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f381,f386]) ).
fof(f416,plain,
~ leq(addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),
inference(resolution,[status(thm)],[f192,f101]) ).
fof(f1360,plain,
! [X0,X1] : addition(multiplication(X0,X1),strong_iteration(X0)) = addition(multiplication(X0,addition(X1,strong_iteration(X0))),one),
inference(paramodulation,[status(thm)],[f37,f114]) ).
fof(f1516,plain,
~ leq(addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),addition(multiplication(sK0_skl,addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl))),one)),
inference(resolution,[status(thm)],[f416,f64]) ).
fof(f1521,plain,
~ leq(addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),addition(multiplication(sK0_skl,multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl))),strong_iteration(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f1360,f1516]) ).
fof(f1817,plain,
! [X0] : addition(strong_iteration(X0),strong_iteration(X0)) = addition(strong_iteration(X0),one),
inference(paramodulation,[status(thm)],[f396,f275]) ).
fof(f1832,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),one),
inference(forward_demodulation,[status(thm)],[f24,f1817]) ).
fof(f2172,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(multiplication(X0,strong_iteration(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f37,f138]) ).
fof(f2265,plain,
~ leq(addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl))),
inference(backward_demodulation,[status(thm)],[f2266,f1521]) ).
fof(f2266,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(X0,multiplication(strong_iteration(X0),X1)),X1),
inference(forward_demodulation,[status(thm)],[f25,f2172]) ).
fof(f2730,plain,
addition(addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)),multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl))) != multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),
inference(resolution,[status(thm)],[f2265,f44]) ).
fof(f2735,plain,
addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),addition(strong_iteration(sK0_skl),multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)))) != multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f22,f2730]) ).
fof(f2736,plain,
addition(multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),strong_iteration(sK0_skl)) != multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),
inference(forward_demodulation,[status(thm)],[f275,f2735]) ).
fof(f3143,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(strong_iteration(X0),X1),X1),
inference(paramodulation,[status(thm)],[f1832,f138]) ).
fof(f3178,plain,
multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)) != multiplication(strong_iteration(sK0_skl),strong_iteration(sK0_skl)),
inference(backward_demodulation,[status(thm)],[f3143,f2736]) ).
fof(f3193,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 22:46:06 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.23/1.15 % Refutation found
% 0.23/1.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.38/1.19 % Elapsed time: 0.708396 seconds
% 0.38/1.19 % CPU time: 4.526731 seconds
% 0.38/1.19 % Total memory used: 112.791 MB
% 0.38/1.19 % Net memory used: 111.564 MB
%------------------------------------------------------------------------------