%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE178+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:58:29 PM UTC 2026
% Result : Satisfiable 0.11s 0.37s
% Output : Saturation 0.11s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
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(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,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,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [A,B,C] :
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f44,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f45,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f46,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f47,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f75,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f36,f25]) ).
fof(f76,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f36,f52]) ).
fof(f79,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f22,f36]) ).
fof(f86,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f92,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f94,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f25,f23]) ).
fof(f96,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f23,f36]) ).
fof(f104,plain,
! [X0] : leq(domain(X0),one),
inference(resolution,[status(thm)],[f45,f36]) ).
fof(f105,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(paramodulation,[status(thm)],[f22,f45]) ).
fof(f108,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f45,f23]) ).
fof(f109,plain,
! [X0] :
( one != one
| leq(domain(X0),one) ),
inference(paramodulation,[status(thm)],[f45,f36]) ).
fof(f112,definition,
! [X0] :
( sQ0_spl
<=> leq(domain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f115,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f112,f115]) ).
fof(f124,plain,
! [X0] :
( one != domain(X0)
| leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f45,f79]) ).
fof(f125,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f23,f79]) ).
fof(f153,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f105,f23]) ).
fof(f156,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f94,f36]) ).
fof(f165,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f94]) ).
fof(f170,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f94,f79]) ).
fof(f188,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f156]) ).
fof(f192,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f156]) ).
fof(f195,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f192,f35]) ).
fof(f198,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f23,f192]) ).
fof(f205,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f198,f35]) ).
fof(f206,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f23,f198]) ).
fof(f209,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f22,f198]) ).
fof(f212,plain,
! [X0,X1] : leq(domain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f105,f198]) ).
fof(f221,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f23,f209]) ).
fof(f223,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f29]) ).
fof(f230,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f235,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f236,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f29,f198]) ).
fof(f237,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f29,f192]) ).
fof(f238,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f29,f156]) ).
fof(f240,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f29,f79]) ).
fof(f241,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f29,f23]) ).
fof(f242,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f29,f36]) ).
fof(f262,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f221,f35]) ).
fof(f263,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f23,f221]) ).
fof(f269,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f29,f221]) ).
fof(f272,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f23,f221]) ).
fof(f282,plain,
! [X0,X1] : addition(domain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f212,f35]) ).
fof(f285,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f23,f212]) ).
fof(f287,plain,
! [X0,X1] : leq(domain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f22,f212]) ).
fof(f299,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f23,f165]) ).
fof(f305,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f23,f165]) ).
fof(f320,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f165,f198]) ).
fof(f321,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f165,f192]) ).
fof(f324,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f165,f79]) ).
fof(f325,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f165,f23]) ).
fof(f328,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f205,f299]) ).
fof(f329,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f23,f328]) ).
fof(f347,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f23,f325]) ).
fof(f348,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f329,f347]) ).
fof(f350,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f29,f321]) ).
fof(f353,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f321]) ).
fof(f364,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f23,f321]) ).
fof(f375,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f29,f350]) ).
fof(f396,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f22,f30]) ).
fof(f399,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f26,f30]) ).
fof(f401,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f404,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f26,f30]) ).
fof(f406,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f410,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f30,f321]) ).
fof(f413,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f30,f221]) ).
fof(f414,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f30,f198]) ).
fof(f415,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f30,f192]) ).
fof(f416,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f30,f156]) ).
fof(f418,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f30,f79]) ).
fof(f419,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f30,f23]) ).
fof(f420,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f30,f36]) ).
fof(f434,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f30,f410]) ).
fof(f441,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f195]) ).
fof(f449,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f23,f195]) ).
fof(f455,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f22,f195]) ).
fof(f473,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f195,f79]) ).
fof(f476,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f305,f441]) ).
fof(f483,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f476,f449]) ).
fof(f507,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f455]) ).
fof(f543,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f455,f79]) ).
fof(f547,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f507]) ).
fof(f548,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),X1)) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f329,f547]) ).
fof(f549,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X1))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f548]) ).
fof(f550,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f195,f549]) ).
fof(f592,plain,
( one != zero
| leq(one,domain(zero)) ),
inference(paramodulation,[status(thm)],[f46,f124]) ).
fof(f593,definition,
( sQ2_spl
<=> leq(one,domain(zero)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( ~ sQ2_spl
| leq(one,domain(zero)) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,definition,
( sQ3_spl
<=> one = zero ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f592,f593,f596]) ).
fof(f600,plain,
( ~ sQ2_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f46,f594]) ).
fof(f601,plain,
( ~ sQ2_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f600,f35]) ).
fof(f603,plain,
! [X0] :
( ~ sQ2_spl
| leq(one,X0) ),
inference(backward_demodulation,[status(thm)],[f609,f76]) ).
fof(f604,plain,
! [X0] :
( ~ sQ2_spl
| multiplication(zero,X0) = one ),
inference(backward_demodulation,[status(thm)],[f609,f32]) ).
fof(f609,plain,
( ~ sQ2_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f24,f601]) ).
fof(f610,plain,
! [X0] :
( ~ sQ2_spl
| multiplication(one,X0) = one ),
inference(forward_demodulation,[status(thm)],[f609,f604]) ).
fof(f642,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f30,f40]) ).
fof(f643,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f29,f40]) ).
fof(f644,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(multiplication(X1,X2),X0)),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f455,f40]) ).
fof(f645,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X0,multiplication(X1,X2))),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f195,f40]) ).
fof(f646,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(X2,multiplication(X0,X1))),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f165,f40]) ).
fof(f647,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(multiplication(X0,X1),X2)),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f94,f40]) ).
fof(f648,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f22,f40]) ).
fof(f650,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f25,f40]) ).
fof(f651,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f652,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f28,f40]) ).
fof(f653,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f27,f40]) ).
fof(f731,plain,
! [X0] :
( ~ sQ2_spl
| X0 = one ),
inference(paramodulation,[status(thm)],[f28,f610]) ).
fof(f749,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f30,f42]) ).
fof(f750,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f29,f42]) ).
fof(f752,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X1,X2),X0),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f455,f42]) ).
fof(f753,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f195,f42]) ).
fof(f754,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,multiplication(X0,X1)),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f165,f42]) ).
fof(f755,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f94,f42]) ).
fof(f756,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f22,f42]) ).
fof(f758,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f25,f42]) ).
fof(f759,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f26,f42]) ).
fof(f760,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f28,f42]) ).
fof(f761,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f27,f42]) ).
fof(f762,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f26,f749]) ).
fof(f763,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f26,f750]) ).
fof(f765,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f26,f758]) ).
fof(f768,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f731,f731]) ).
fof(f771,plain,
! [X0,X1] :
( ~ sQ2_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f731,f603]) ).
fof(model,axiom,
( sQ0_spl
| sQ2_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE178+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n005.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Sun Sep 20 22:49:48 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Drodi V4.1.1
% 0.11/0.37 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.11/0.37 % SZS output start Saturation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.054505 seconds
% 0.11/0.39 % CPU time: 0.216122 seconds
% 0.11/0.39 % Total memory used: 4.379 MB
% 0.11/0.39 % Net memory used: 4.133 MB
%------------------------------------------------------------------------------