%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:57:44 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 31 unt; 0 def)
% Number of atoms : 148 ( 57 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 153 ( 77 ~; 49 |; 20 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 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 ( 75 !; 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(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = 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(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(f14,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') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,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)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ! [X0,X1] :
( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( ( ~ leq(addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) )
& test(sK1_skl)
& test(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f52]) ).
fof(f54,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f58,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f27,f56]) ).
fof(f59,plain,
( ~ leq(addition(addition(addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f27,f58]) ).
fof(f66,plain,
( ~ leq(addition(addition(addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(paramodulation,[status(thm)],[f19,f59]) ).
fof(f75,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f57]) ).
fof(f78,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f75,f55]) ).
fof(f79,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f75,f54]) ).
fof(f81,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f78]) ).
fof(f85,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(paramodulation,[status(thm)],[f19,f79]) ).
fof(f93,plain,
( ~ leq(addition(addition(addition(multiplication(one,sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(backward_demodulation,[status(thm)],[f85,f66]) ).
fof(f108,plain,
( ~ leq(addition(addition(addition(multiplication(one,sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),multiplication(one,sK1_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f85,f93]) ).
fof(f109,plain,
( ~ leq(addition(addition(addition(multiplication(one,sK1_skl),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),sK1_skl),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f25,f108]) ).
fof(f110,plain,
( ~ leq(addition(addition(addition(sK1_skl,multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),sK1_skl),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(forward_demodulation,[status(thm)],[f25,f109]) ).
fof(f123,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f218,plain,
addition(c(sK2_skl),sK2_skl) = addition(one,sK2_skl),
inference(paramodulation,[status(thm)],[f79,f123]) ).
fof(f236,plain,
one = addition(one,sK2_skl),
inference(forward_demodulation,[status(thm)],[f79,f218]) ).
fof(f240,plain,
one = addition(sK2_skl,one),
inference(paramodulation,[status(thm)],[f19,f236]) ).
fof(f339,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f345,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f349,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(addition(X0,multiplication(X1,X2)),multiplication(X1,X3)),
inference(paramodulation,[status(thm)],[f26,f20]) ).
fof(f359,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1_skl,sK2_skl),sK1_skl),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))) ),
inference(backward_demodulation,[status(thm)],[f339,f110]) ).
fof(f377,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(addition(multiplication(sK1_skl,sK2_skl),sK1_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f349,f359]) ).
fof(f378,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(multiplication(sK1_skl,addition(sK2_skl,one)),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f345,f377]) ).
fof(f379,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(multiplication(sK1_skl,one),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f240,f378]) ).
fof(f380,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(sK1_skl,multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))) ),
inference(forward_demodulation,[status(thm)],[f24,f379]) ).
fof(f381,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(sK1_skl,multiplication(c(sK1_skl),one))) ),
inference(forward_demodulation,[status(thm)],[f85,f380]) ).
fof(f382,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,addition(sK1_skl,c(sK1_skl))) ),
inference(forward_demodulation,[status(thm)],[f24,f381]) ).
fof(f383,plain,
( ~ leq(addition(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f81,f382]) ).
fof(f384,plain,
( ~ leq(addition(multiplication(sK1_skl,addition(one,sK2_skl)),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f349,f383]) ).
fof(f385,plain,
( ~ leq(addition(multiplication(sK1_skl,one),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f236,f384]) ).
fof(f386,plain,
( ~ leq(addition(sK1_skl,multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f24,f385]) ).
fof(f387,plain,
( ~ leq(addition(sK1_skl,multiplication(c(sK1_skl),one)),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f85,f386]) ).
fof(f388,plain,
( ~ leq(addition(sK1_skl,c(sK1_skl)),one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f24,f387]) ).
fof(f389,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(forward_demodulation,[status(thm)],[f81,f388]) ).
fof(f390,plain,
~ leq(one,one),
inference(duplicate_literals_removal,[status(thm)],[f389]) ).
fof(f497,plain,
addition(one,one) != one,
inference(resolution,[status(thm)],[f390,f33]) ).
fof(f498,plain,
one != one,
inference(forward_demodulation,[status(thm)],[f22,f497]) ).
fof(f499,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:40:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.49 % Elapsed time: 0.111118 seconds
% 0.14/0.49 % CPU time: 0.579970 seconds
% 0.14/0.49 % Total memory used: 112.575 MB
% 0.14/0.49 % Net memory used: 112.004 MB
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