%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE063+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:57:53 PM UTC 2026
% Result : Theorem 0.14s 0.84s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 45 unt; 0 def)
% Number of atoms : 67 ( 47 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 ( 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 : 88 ( 86 !; 2 ?)
% 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/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/sandbox2/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(f25,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(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(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
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(f79,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f191,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f79,f34]) ).
fof(f224,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f27,f191]) ).
fof(f248,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f28,f191]) ).
fof(f372,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f383,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f372]) ).
fof(f483,plain,
! [X0,X1] : leq(domain(X0),domain(addition(X0,X1))),
inference(paramodulation,[status(thm)],[f39,f191]) ).
fof(f768,plain,
domain(addition(sK0_skl,sK1_skl)) != domain(sK1_skl),
inference(forward_demodulation,[status(thm)],[f39,f43]) ).
fof(f2597,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f37,f224]) ).
fof(f2621,plain,
! [X0,X1] : leq(multiplication(X0,domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f25,f2597]) ).
fof(f2623,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),X0) = X0,
inference(resolution,[status(thm)],[f2621,f33]) ).
fof(f2705,plain,
! [X0,X1] : leq(domain(multiplication(X0,domain(X1))),domain(X0)),
inference(paramodulation,[status(thm)],[f2623,f483]) ).
fof(f2729,plain,
! [X0,X1] : leq(domain(multiplication(X0,X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f36,f2705]) ).
fof(f3699,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),multiplication(one,X1)),
inference(paramodulation,[status(thm)],[f37,f248]) ).
fof(f3729,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f26,f3699]) ).
fof(f3891,plain,
! [X0,X1] : addition(multiplication(domain(X0),X1),X1) = X1,
inference(resolution,[status(thm)],[f3729,f33]) ).
fof(f3925,plain,
! [X0,X1] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f3891]) ).
fof(f4026,plain,
sK0_skl = multiplication(domain(sK1_skl),sK0_skl),
inference(backward_demodulation,[status(thm)],[f3925,f42]) ).
fof(f4203,plain,
leq(domain(sK0_skl),domain(domain(sK1_skl))),
inference(paramodulation,[status(thm)],[f4026,f2729]) ).
fof(f4212,plain,
leq(domain(sK0_skl),domain(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f383,f4203]) ).
fof(f4213,plain,
addition(domain(sK0_skl),domain(sK1_skl)) = domain(sK1_skl),
inference(resolution,[status(thm)],[f4212,f33]) ).
fof(f4214,plain,
domain(addition(sK0_skl,sK1_skl)) = domain(sK1_skl),
inference(forward_demodulation,[status(thm)],[f39,f4213]) ).
fof(f4215,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4214,f768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE063+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n011.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sun Sep 20 22:41:55 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.56 % Drodi V4.1.1
% 0.14/0.84 % Refutation found
% 0.14/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.86 % Elapsed time: 0.294115 seconds
% 0.14/0.86 % CPU time: 2.115519 seconds
% 0.14/0.86 % Total memory used: 97.580 MB
% 0.14/0.86 % Net memory used: 96.039 MB
%------------------------------------------------------------------------------