%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE062+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 : n002.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 27.12s 3.89s
% Output : CNFRefutation 26.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of formulae : 91 ( 91 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 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 : 154 ( 152 !; 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(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(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
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] : multiplication(domain(X0),domain(X1)) = multiplication(domain(X1),domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] : multiplication(domain(X0),domain(X1)) = multiplication(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(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(f24,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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),domain(X1)) != multiplication(domain(X1),domain(X0)),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
multiplication(domain(sK0_skl),domain(sK1_skl)) != multiplication(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),domain(sK1_skl)) != multiplication(domain(sK1_skl),domain(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f204,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f207,plain,
addition(one,domain(one)) = domain(one),
inference(forward_demodulation,[status(thm)],[f25,f204]) ).
fof(f217,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f234,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f217]) ).
fof(f287,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)),
inference(paramodulation,[status(thm)],[f39,f20]) ).
fof(f303,plain,
! [X0,X1] : domain(addition(X0,X1)) = domain(addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f287]) ).
fof(f325,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f347,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f1207,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f325]) ).
fof(f1260,plain,
addition(domain(one),domain(one)) = addition(domain(one),one),
inference(paramodulation,[status(thm)],[f207,f1207]) ).
fof(f1291,plain,
domain(addition(one,one)) = addition(domain(one),one),
inference(forward_demodulation,[status(thm)],[f39,f1260]) ).
fof(f1292,plain,
domain(one) = addition(domain(one),one),
inference(forward_demodulation,[status(thm)],[f23,f1291]) ).
fof(f1296,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f37,f1292]) ).
fof(f1372,plain,
! [X0] : domain(addition(X0,one)) = addition(domain(X0),one),
inference(paramodulation,[status(thm)],[f1296,f39]) ).
fof(f1373,plain,
! [X0] : domain(addition(one,X0)) = addition(one,domain(X0)),
inference(paramodulation,[status(thm)],[f1296,f39]) ).
fof(f1423,plain,
! [X0] : domain(addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f37,f1372]) ).
fof(f1429,plain,
! [X0] : domain(addition(one,X0)) = one,
inference(paramodulation,[status(thm)],[f303,f1423]) ).
fof(f1478,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f1373,f1429]) ).
fof(f1639,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f20,f28]) ).
fof(f1642,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f1646,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f1666,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f28,f1639]) ).
fof(f5289,plain,
! [X0,X1] : multiplication(X0,one) = addition(multiplication(X0,domain(X1)),X0),
inference(paramodulation,[status(thm)],[f37,f347]) ).
fof(f5406,plain,
! [X0,X1] : X0 = addition(multiplication(X0,domain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f25,f5289]) ).
fof(f5700,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f1666,f1642]) ).
fof(f5725,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f1642]) ).
fof(f5830,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f1478,f5725]) ).
fof(f5874,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f5830]) ).
fof(f6111,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,X0)) = addition(multiplication(domain(X0),X1),X0),
inference(paramodulation,[status(thm)],[f5874,f27]) ).
fof(f6112,plain,
! [X0,X1] : multiplication(domain(X0),addition(X0,X1)) = addition(X0,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f5874,f27]) ).
fof(f6313,plain,
! [X0,X1] : multiplication(one,X0) = addition(multiplication(multiplication(one,domain(X1)),X0),X0),
inference(paramodulation,[status(thm)],[f5406,f1646]) ).
fof(f6419,plain,
! [X0,X1] : X0 = addition(multiplication(multiplication(one,domain(X1)),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f6313]) ).
fof(f6420,plain,
! [X0,X1] : X0 = addition(multiplication(one,multiplication(domain(X1),X0)),X0),
inference(forward_demodulation,[status(thm)],[f24,f6419]) ).
fof(f6421,plain,
! [X0,X1] : X0 = addition(multiplication(domain(X1),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f6420]) ).
fof(f7868,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,f6111]) ).
fof(f7965,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = addition(multiplication(domain(domain(X0)),domain(X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f234,f7868]) ).
fof(f7966,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = addition(multiplication(domain(X0),domain(X1)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f234,f7965]) ).
fof(f7967,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X1,X0))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f5406,f7966]) ).
fof(f8073,plain,
! [X0,X1] : multiplication(domain(X0),domain(addition(X0,X1))) = domain(X0),
inference(paramodulation,[status(thm)],[f303,f7967]) ).
fof(f8246,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),domain(X1)) = domain(multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f6421,f8073]) ).
fof(f8247,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,domain(X1))),domain(X0)) = domain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f5406,f8073]) ).
fof(f8286,plain,
! [X0,X1] : domain(multiplication(domain(X0),addition(X0,X1))) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f8073,f36]) ).
fof(f8343,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),domain(X0)) = domain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f36,f8247]) ).
fof(f8344,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),domain(X0)) = domain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f36,f8343]) ).
fof(f8373,plain,
! [X0,X1] : domain(addition(X0,multiplication(domain(X0),X1))) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f6112,f8286]) ).
fof(f8375,plain,
! [X0,X1] : domain(addition(X0,multiplication(domain(X0),X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f234,f8373]) ).
fof(f11049,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),X1) = addition(multiplication(domain(X0),X1),multiplication(domain(multiplication(domain(X0),X1)),X1)),
inference(paramodulation,[status(thm)],[f6421,f6112]) ).
fof(f11171,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),X1) = multiplication(addition(domain(X0),domain(multiplication(domain(X0),X1))),X1),
inference(forward_demodulation,[status(thm)],[f28,f11049]) ).
fof(f11172,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),X1) = multiplication(domain(addition(X0,multiplication(domain(X0),X1))),X1),
inference(forward_demodulation,[status(thm)],[f39,f11171]) ).
fof(f11173,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),X1) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f8375,f11172]) ).
fof(f11322,plain,
! [X0,X1] : multiplication(domain(multiplication(domain(X0),X1)),domain(X1)) = multiplication(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f36,f11173]) ).
fof(f11444,plain,
! [X0,X1] : domain(multiplication(domain(X0),X1)) = multiplication(domain(X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f8246,f11322]) ).
fof(f12010,plain,
! [X0,X1] : multiplication(multiplication(domain(X0),domain(X1)),domain(domain(X0))) = domain(multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f11444,f8344]) ).
fof(f12109,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(domain(X1),domain(domain(X0)))) = domain(multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f24,f12010]) ).
fof(f12110,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(domain(X1),domain(X0))) = domain(multiplication(domain(X0),X1)),
inference(forward_demodulation,[status(thm)],[f234,f12109]) ).
fof(f12112,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(domain(X1),domain(X0))) = multiplication(domain(X0),domain(X1)),
inference(forward_demodulation,[status(thm)],[f11444,f12110]) ).
fof(f28825,plain,
! [X0,X1] : multiplication(domain(X0),domain(X1)) = addition(multiplication(domain(X1),domain(X0)),multiplication(domain(X0),domain(X1))),
inference(paramodulation,[status(thm)],[f12112,f6421]) ).
fof(f28851,plain,
! [X0,X1] : multiplication(addition(domain(X0),one),multiplication(domain(X1),domain(X0))) = addition(multiplication(domain(X1),domain(X0)),multiplication(domain(X0),domain(X1))),
inference(paramodulation,[status(thm)],[f12112,f5700]) ).
fof(f29120,plain,
! [X0,X1] : multiplication(one,multiplication(domain(X0),domain(X1))) = addition(multiplication(domain(X0),domain(X1)),multiplication(domain(X1),domain(X0))),
inference(forward_demodulation,[status(thm)],[f37,f28851]) ).
fof(f29121,plain,
! [X0,X1] : multiplication(domain(X0),domain(X1)) = addition(multiplication(domain(X0),domain(X1)),multiplication(domain(X1),domain(X0))),
inference(forward_demodulation,[status(thm)],[f26,f29120]) ).
fof(f29123,plain,
! [X0,X1] : multiplication(domain(X0),domain(X1)) = multiplication(domain(X1),domain(X0)),
inference(forward_demodulation,[status(thm)],[f28825,f29121]) ).
fof(f29124,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f42,f29123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE062+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:44:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 27.12/3.89 % Refutation found
% 27.12/3.89 % SZS status Theorem for theBenchmark: Theorem is valid
% 27.12/3.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.97/3.97 % Elapsed time: 3.601525 seconds
% 26.97/3.97 % CPU time: 28.312138 seconds
% 26.97/3.97 % Total memory used: 341.069 MB
% 26.97/3.97 % Net memory used: 334.682 MB
%------------------------------------------------------------------------------