%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE069+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 : n010.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 1.13s 1.05s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,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(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
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] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
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] : multiplication(domain(X0),addition(domain(X0),domain(X1))) != domain(X0),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
multiplication(domain(sK0_skl),addition(domain(sK0_skl),domain(sK1_skl))) != domain(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,
multiplication(domain(sK0_skl),addition(domain(sK0_skl),domain(sK1_skl))) != domain(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
multiplication(domain(sK0_skl),domain(addition(sK0_skl,sK1_skl))) != domain(sK0_skl),
inference(forward_demodulation,[status(thm)],[f39,f42]) ).
fof(f48,plain,
multiplication(domain(sK0_skl),domain(addition(sK1_skl,sK0_skl))) != domain(sK0_skl),
inference(paramodulation,[status(thm)],[f20,f43]) ).
fof(f300,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f308,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f402,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(paramodulation,[status(thm)],[f20,f37]) ).
fof(f437,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f444,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f437]) ).
fof(f1322,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f308]) ).
fof(f1370,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f402,f1322]) ).
fof(f1380,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f1370]) ).
fof(f1436,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f1380,f27]) ).
fof(f2674,plain,
! [X0,X1] : multiplication(domain(domain(X0)),domain(addition(X1,X0))) = addition(multiplication(domain(domain(X0)),domain(X1)),domain(X0)),
inference(paramodulation,[status(thm)],[f39,f1436]) ).
fof(f2726,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = addition(multiplication(domain(domain(X0)),domain(X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f444,f2674]) ).
fof(f2727,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = addition(multiplication(domain(X0),domain(X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f444,f2726]) ).
fof(f2934,plain,
! [X0,X1] : multiplication(X0,one) = addition(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f37,f300]) ).
fof(f3025,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = domain(X0),
inference(backward_demodulation,[status(thm)],[f3026,f2727]) ).
fof(f3026,plain,
! [X0,X1] : X0 = addition(multiplication(X0,domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f25,f2934]) ).
fof(f3096,plain,
domain(sK0_skl) != domain(sK0_skl),
inference(backward_demodulation,[status(thm)],[f3025,f48]) ).
fof(f3097,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n010.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 22:41:56 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 1.13/1.05 % Refutation found
% 1.13/1.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.13/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.13/1.10 % Elapsed time: 0.648500 seconds
% 1.13/1.10 % CPU time: 4.772209 seconds
% 1.13/1.10 % Total memory used: 105.040 MB
% 1.13/1.10 % Net memory used: 103.632 MB
%------------------------------------------------------------------------------