%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE093+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 : n015.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 12:57:57 PM UTC 2026
% Result : Theorem 0.17s 0.58s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 55 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 5 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 62 !; 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [X0] : domain(star(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [X0] : domain(star(X0)) = one,
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f29,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
? [X0] : domain(star(X0)) != one,
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f51,plain,
domain(star(sK0_skl)) != one,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f50]) ).
fof(f52,plain,
domain(star(sK0_skl)) != one,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f30,f46]) ).
fof(f58,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f30,f55]) ).
fof(f65,plain,
! [X0,X1] : domain(addition(domain(X0),X1)) = addition(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f58,f49]) ).
fof(f69,plain,
! [X0,X1] : domain(addition(domain(X0),X1)) = domain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f49,f65]) ).
fof(f97,plain,
! [X0] : one = addition(one,domain(X0)),
inference(paramodulation,[status(thm)],[f47,f24]) ).
fof(f162,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f189,plain,
! [X0] : domain(one) = domain(addition(X0,one)),
inference(paramodulation,[status(thm)],[f47,f69]) ).
fof(f221,plain,
! [X0] : domain(one) = domain(addition(one,X0)),
inference(paramodulation,[status(thm)],[f24,f189]) ).
fof(f274,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramodulation,[status(thm)],[f29,f45]) ).
fof(f286,plain,
one = multiplication(domain(one),one),
inference(forward_demodulation,[status(thm)],[f97,f274]) ).
fof(f287,plain,
! [X0] : one = domain(addition(one,X0)),
inference(backward_demodulation,[status(thm)],[f291,f221]) ).
fof(f291,plain,
one = domain(one),
inference(forward_demodulation,[status(thm)],[f29,f286]) ).
fof(f350,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f37,f40]) ).
fof(f352,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f25,f350]) ).
fof(f353,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = star(X0),
inference(forward_demodulation,[status(thm)],[f162,f352]) ).
fof(f3502,plain,
! [X0] : one = domain(star(X0)),
inference(paramodulation,[status(thm)],[f353,f287]) ).
fof(f3537,plain,
one != one,
inference(backward_demodulation,[status(thm)],[f3502,f52]) ).
fof(f3582,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 22:45:50 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.58 % Refutation found
% 0.17/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.64 % Elapsed time: 0.186454 seconds
% 0.17/0.64 % CPU time: 0.945041 seconds
% 0.17/0.64 % Total memory used: 70.514 MB
% 0.17/0.64 % Net memory used: 70.059 MB
%------------------------------------------------------------------------------