%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE181+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:58:32 PM UTC 2026
% Result : Satisfiable 0.19s 0.48s
% Output : Saturation 0.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(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(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(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
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(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
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(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : multiplication(A,omega(A)) = omega(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( leq(A,addition(multiplication(B,A),C))
=> leq(A,addition(omega(B),multiplication(star(B),C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f26,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f32,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
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(f38,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f41,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(f42,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,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(f44,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0] : multiplication(X0,omega(X0)) = omega(X0),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
! [A,B,C] :
( leq(A,addition(omega(B),multiplication(star(B),C)))
| ~ leq(A,addition(multiplication(B,A),C)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0,X1,X2] :
( leq(X0,addition(omega(X1),multiplication(star(X1),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f57,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f26,f24]) ).
fof(f80,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f38,f27]) ).
fof(f81,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f38,f57]) ).
fof(f84,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f24,f38]) ).
fof(f91,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f25]) ).
fof(f97,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f24,f25]) ).
fof(f99,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f27,f25]) ).
fof(f101,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f25,f38]) ).
fof(f109,plain,
zero = omega(zero),
inference(paramodulation,[status(thm)],[f34,f45]) ).
fof(f115,plain,
! [X0] : leq(domain(X0),one),
inference(resolution,[status(thm)],[f50,f38]) ).
fof(f116,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(paramodulation,[status(thm)],[f24,f50]) ).
fof(f119,plain,
! [X0,X1] : addition(domain(X0),addition(one,X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f50,f25]) ).
fof(f120,plain,
! [X0] :
( one != one
| leq(domain(X0),one) ),
inference(paramodulation,[status(thm)],[f50,f38]) ).
fof(f123,definition,
! [X0] :
( sQ0_spl
<=> leq(domain(X0),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f126,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f123,f126]) ).
fof(f130,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,omega(multiplication(X0,X1)))) = omega(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f45,f28]) ).
fof(f136,plain,
! [X0,X1] : multiplication(X0,multiplication(omega(X0),X1)) = multiplication(omega(X0),X1),
inference(paramodulation,[status(thm)],[f45,f28]) ).
fof(f154,plain,
! [X0] :
( one != domain(X0)
| leq(one,domain(X0)) ),
inference(paramodulation,[status(thm)],[f50,f84]) ).
fof(f155,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f25,f84]) ).
fof(f167,plain,
! [X0,X1] : addition(one,addition(domain(X0),X1)) = addition(one,X1),
inference(paramodulation,[status(thm)],[f116,f25]) ).
fof(f170,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f99,f38]) ).
fof(f179,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f99]) ).
fof(f184,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f99,f84]) ).
fof(f202,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f25,f170]) ).
fof(f206,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f24,f170]) ).
fof(f209,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f31]) ).
fof(f215,plain,
! [X0,X1] : multiplication(X0,addition(omega(X0),X1)) = addition(omega(X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f45,f31]) ).
fof(f217,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f221,plain,
! [X0,X1] : multiplication(X0,addition(X1,omega(X0))) = addition(multiplication(X0,X1),omega(X0)),
inference(paramodulation,[status(thm)],[f45,f31]) ).
fof(f223,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f224,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f31,f170]) ).
fof(f226,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f31,f84]) ).
fof(f227,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)],[f31,f25]) ).
fof(f228,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f31,f38]) ).
fof(f248,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f206,f37]) ).
fof(f249,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f31,f206]) ).
fof(f252,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f25,f206]) ).
fof(f259,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f252,f37]) ).
fof(f260,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f25,f252]) ).
fof(f263,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f24,f252]) ).
fof(f266,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f31,f252]) ).
fof(f267,plain,
! [X0,X1] : leq(domain(X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f116,f252]) ).
fof(f276,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f25,f263]) ).
fof(f278,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f276,f37]) ).
fof(f279,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f25,f276]) ).
fof(f285,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f31,f276]) ).
fof(f288,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f25,f276]) ).
fof(f298,plain,
! [X0,X1] : addition(domain(X0),addition(X1,one)) = addition(X1,one),
inference(resolution,[status(thm)],[f267,f37]) ).
fof(f301,plain,
! [X0,X1,X2] : leq(domain(X0),addition(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f25,f267]) ).
fof(f303,plain,
! [X0,X1] : leq(domain(X0),addition(one,X1)),
inference(paramodulation,[status(thm)],[f24,f267]) ).
fof(f315,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f24,f32]) ).
fof(f318,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)],[f28,f32]) ).
fof(f320,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f321,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X0)) = addition(omega(X0),multiplication(X1,omega(X0))),
inference(paramodulation,[status(thm)],[f45,f32]) ).
fof(f324,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)],[f28,f32]) ).
fof(f326,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f327,plain,
! [X0,X1] : multiplication(addition(X0,X1),omega(X1)) = addition(multiplication(X0,omega(X1)),omega(X1)),
inference(paramodulation,[status(thm)],[f45,f32]) ).
fof(f331,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f32,f276]) ).
fof(f332,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f32,f252]) ).
fof(f333,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f32,f206]) ).
fof(f334,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f32,f170]) ).
fof(f336,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f32,f84]) ).
fof(f337,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)],[f32,f25]) ).
fof(f338,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f32,f38]) ).
fof(f355,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f25,f179]) ).
fof(f362,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f25,f179]) ).
fof(f377,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f179,f252]) ).
fof(f378,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f179,f206]) ).
fof(f381,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f179,f84]) ).
fof(f382,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f179,f25]) ).
fof(f385,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f259,f355]) ).
fof(f386,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f25,f385]) ).
fof(f406,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f25,f382]) ).
fof(f407,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f386,f406]) ).
fof(f409,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f32,f378]) ).
fof(f410,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f31,f378]) ).
fof(f413,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f25,f378]) ).
fof(f425,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f25,f378]) ).
fof(f436,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f32,f409]) ).
fof(f437,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f31,f410]) ).
fof(f459,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f248]) ).
fof(f467,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f25,f248]) ).
fof(f473,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f24,f248]) ).
fof(f491,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f248,f84]) ).
fof(f494,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f362,f459]) ).
fof(f501,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f494,f467]) ).
fof(f525,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f473]) ).
fof(f561,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f473,f84]) ).
fof(f565,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f525]) ).
fof(f566,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X2),X1)) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f386,f565]) ).
fof(f567,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X1))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f566]) ).
fof(f568,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f248,f567]) ).
fof(f610,plain,
( one != zero
| leq(one,domain(zero)) ),
inference(paramodulation,[status(thm)],[f51,f154]) ).
fof(f611,definition,
( sQ2_spl
<=> leq(one,domain(zero)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ2_spl
| leq(one,domain(zero)) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
( sQ3_spl
<=> one = zero ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f610,f611,f614]) ).
fof(f618,plain,
( ~ sQ2_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f51,f612]) ).
fof(f619,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f620,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f28,f39]) ).
fof(f621,plain,
leq(addition(one,zero),star(zero)),
inference(paramodulation,[status(thm)],[f34,f39]) ).
fof(f622,plain,
leq(addition(one,star(one)),star(one)),
inference(paramodulation,[status(thm)],[f30,f39]) ).
fof(f623,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f25,f619]) ).
fof(f624,plain,
leq(one,star(zero)),
inference(forward_demodulation,[status(thm)],[f26,f621]) ).
fof(f625,plain,
( ~ sQ2_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f618,f37]) ).
fof(f628,plain,
! [X0] :
( ~ sQ2_spl
| leq(one,X0) ),
inference(backward_demodulation,[status(thm)],[f635,f81]) ).
fof(f629,plain,
! [X0] :
( ~ sQ2_spl
| multiplication(zero,X0) = one ),
inference(backward_demodulation,[status(thm)],[f635,f34]) ).
fof(f635,plain,
( ~ sQ2_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f26,f625]) ).
fof(f637,plain,
! [X0] :
( ~ sQ2_spl
| multiplication(one,X0) = one ),
inference(forward_demodulation,[status(thm)],[f635,f629]) ).
fof(f679,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f32,f42]) ).
fof(f680,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f31,f42]) ).
fof(f681,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)],[f473,f42]) ).
fof(f682,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)],[f248,f42]) ).
fof(f683,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)],[f179,f42]) ).
fof(f684,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)],[f99,f42]) ).
fof(f685,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f24,f42]) ).
fof(f687,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f27,f42]) ).
fof(f688,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)],[f28,f42]) ).
fof(f689,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f30,f42]) ).
fof(f690,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),omega(X0))
| ~ leq(addition(omega(X0),X1),omega(X0)) ),
inference(paramodulation,[status(thm)],[f45,f42]) ).
fof(f691,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f29,f42]) ).
fof(f768,plain,
! [X0] :
( ~ sQ2_spl
| X0 = one ),
inference(paramodulation,[status(thm)],[f30,f637]) ).
fof(f790,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f768,f768]) ).
fof(f793,plain,
! [X0,X1] :
( ~ sQ2_spl
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f768,f628]) ).
fof(model,axiom,
( sQ0_spl
| sQ2_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE181+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n006.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:49:27 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 0.19/0.48 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.19/0.48 % SZS output start Saturation for theBenchmark
% See solution above
% 0.23/0.51 % Elapsed time: 0.051723 seconds
% 0.23/0.51 % CPU time: 0.240048 seconds
% 0.23/0.51 % Total memory used: 4.813 MB
% 0.23/0.51 % Net memory used: 4.576 MB
%------------------------------------------------------------------------------