%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE092+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 : n012.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 46.33s 6.24s
% Output : CNFRefutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 142 ( 117 unt; 0 def)
% Number of atoms : 171 ( 140 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 33 ~; 26 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 184 ( 183 !; 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0] : X0 = multiplication(X0,one),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0] : X0 = multiplication(one,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
? [X0] : domain(coantidomain(X0)) != coantidomain(X0),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
domain(coantidomain(sK0_skl)) != coantidomain(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f46]) ).
fof(f48,plain,
coantidomain(sK0_skl) != domain(coantidomain(sK0_skl)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f59,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f25,f23]) ).
fof(f78,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f38,f28]) ).
fof(f83,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = addition(X0,X1) ),
inference(paramodulation,[status(thm)],[f23,f36]) ).
fof(f86,plain,
coantidomain(one) = zero,
inference(paramodulation,[status(thm)],[f29,f42]) ).
fof(f92,plain,
one = addition(antidomain(zero),antidomain(one)),
inference(paramodulation,[status(thm)],[f78,f40]) ).
fof(f97,plain,
one = addition(antidomain(zero),zero),
inference(forward_demodulation,[status(thm)],[f78,f92]) ).
fof(f98,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f25,f97]) ).
fof(f108,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f41,f40]) ).
fof(f115,plain,
! [X0] : codomain(coantidomain(X0)) = coantidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f45,f45]) ).
fof(f116,plain,
coantidomain(zero) = codomain(one),
inference(paramodulation,[status(thm)],[f86,f45]) ).
fof(f118,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f37,f59]) ).
fof(f140,plain,
! [X0,X1] : addition(multiplication(antidomain(X0),X1),zero) = multiplication(antidomain(X0),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f38,f30]) ).
fof(f147,plain,
! [X0,X1,X2] :
( multiplication(X0,X2) = multiplication(X0,addition(X1,X2))
| ~ leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f30,f36]) ).
fof(f155,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f25,f140]) ).
fof(f185,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f45,f43]) ).
fof(f186,plain,
! [X0,X1] : coantidomain(multiplication(codomain(X0),X1)) = addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(codomain(X0),X1))),
inference(forward_demodulation,[status(thm)],[f45,f185]) ).
fof(f188,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X0)),X0))) = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f38,f186]) ).
fof(f191,plain,
! [X0] : addition(coantidomain(zero),coantidomain(multiplication(codomain(X0),coantidomain(X0)))) = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(paramodulation,[status(thm)],[f42,f186]) ).
fof(f227,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(paramodulation,[status(thm)],[f108,f23]) ).
fof(f265,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f29,f31]) ).
fof(f270,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,antidomain(X1)),X1),
inference(paramodulation,[status(thm)],[f38,f31]) ).
fof(f279,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X1,X2))
| multiplication(addition(X0,X1),X2) != multiplication(X1,X2) ),
inference(paramodulation,[status(thm)],[f31,f37]) ).
fof(f285,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f270]) ).
fof(f340,plain,
! [X0] : one = addition(codomain(X0),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f45,f44]) ).
fof(f342,plain,
! [X0] : one = addition(coantidomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f23,f340]) ).
fof(f344,plain,
addition(coantidomain(zero),coantidomain(one)) = one,
inference(paramodulation,[status(thm)],[f116,f340]) ).
fof(f346,plain,
addition(codomain(one),zero) = one,
inference(paramodulation,[status(thm)],[f86,f340]) ).
fof(f355,plain,
codomain(one) = one,
inference(forward_demodulation,[status(thm)],[f25,f346]) ).
fof(f356,plain,
addition(coantidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f86,f344]) ).
fof(f357,plain,
one = coantidomain(zero),
inference(forward_demodulation,[status(thm)],[f25,f356]) ).
fof(f439,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f454,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f26,f24]) ).
fof(f465,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(forward_demodulation,[status(thm)],[f41,f39]) ).
fof(f466,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f41,f465]) ).
fof(f610,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f227,f454]) ).
fof(f613,plain,
! [X0] : addition(coantidomain(X0),one) = addition(coantidomain(X0),codomain(X0)),
inference(paramodulation,[status(thm)],[f342,f454]) ).
fof(f626,plain,
! [X0,X1] :
( addition(X0,X1) = X0
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f454,f83]) ).
fof(f629,plain,
! [X0] : one = addition(antidomain(X0),one),
inference(forward_demodulation,[status(thm)],[f227,f610]) ).
fof(f632,plain,
! [X0] : addition(coantidomain(X0),one) = one,
inference(forward_demodulation,[status(thm)],[f342,f613]) ).
fof(f707,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(paramodulation,[status(thm)],[f629,f23]) ).
fof(f725,plain,
! [X0] : one = addition(codomain(X0),one),
inference(paramodulation,[status(thm)],[f45,f632]) ).
fof(f735,plain,
! [X0] : one = addition(one,coantidomain(X0)),
inference(paramodulation,[status(thm)],[f632,f23]) ).
fof(f1370,plain,
! [X0,X1] :
( multiplication(X0,antidomain(X1)) = multiplication(X0,one)
| ~ leq(multiplication(X0,domain(X1)),multiplication(X0,antidomain(X1))) ),
inference(paramodulation,[status(thm)],[f108,f147]) ).
fof(f1377,plain,
! [X0,X1] :
( multiplication(X0,coantidomain(X1)) = multiplication(X0,one)
| ~ leq(multiplication(X0,codomain(X1)),multiplication(X0,coantidomain(X1))) ),
inference(paramodulation,[status(thm)],[f340,f147]) ).
fof(f1395,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,domain(X1)),multiplication(X0,antidomain(X1)))
| X0 = multiplication(X0,antidomain(X1)) ),
inference(forward_demodulation,[status(thm)],[f28,f1370]) ).
fof(f1396,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,codomain(X1)),multiplication(X0,coantidomain(X1)))
| multiplication(X0,coantidomain(X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f28,f1377]) ).
fof(f1680,plain,
! [X0] : multiplication(antidomain(coantidomain(X0)),one) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(paramodulation,[status(thm)],[f340,f155]) ).
fof(f1728,plain,
! [X0] : antidomain(coantidomain(X0)) = multiplication(antidomain(coantidomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f28,f1680]) ).
fof(f2417,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(X0),coantidomain(X0)))) = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f357,f191]) ).
fof(f2418,plain,
! [X0] : one = coantidomain(multiplication(codomain(X0),coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f735,f2417]) ).
fof(f2442,plain,
! [X0] : multiplication(multiplication(codomain(X0),coantidomain(X0)),one) = zero,
inference(paramodulation,[status(thm)],[f2418,f42]) ).
fof(f2464,plain,
! [X0] : multiplication(codomain(X0),multiplication(coantidomain(X0),one)) = zero,
inference(forward_demodulation,[status(thm)],[f27,f2442]) ).
fof(f2465,plain,
! [X0] : zero = multiplication(codomain(X0),coantidomain(X0)),
inference(forward_demodulation,[status(thm)],[f28,f2464]) ).
fof(f2487,plain,
! [X0] : zero = multiplication(coantidomain(codomain(X0)),coantidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f115,f2465]) ).
fof(f2503,plain,
! [X0] : antidomain(multiplication(codomain(X0),domain(coantidomain(X0)))) = addition(antidomain(zero),antidomain(multiplication(codomain(X0),domain(coantidomain(X0))))),
inference(paramodulation,[status(thm)],[f2465,f466]) ).
fof(f2516,plain,
! [X0] : zero = multiplication(coantidomain(codomain(X0)),codomain(X0)),
inference(forward_demodulation,[status(thm)],[f45,f2487]) ).
fof(f2524,plain,
! [X0] : antidomain(multiplication(codomain(X0),domain(coantidomain(X0)))) = addition(one,antidomain(multiplication(codomain(X0),domain(coantidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f98,f2503]) ).
fof(f2525,plain,
! [X0] : one = antidomain(multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f707,f2524]) ).
fof(f3263,plain,
! [X0] : addition(one,coantidomain(multiplication(codomain(antidomain(X0)),X0))) = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f357,f188]) ).
fof(f3264,plain,
! [X0] : one = coantidomain(multiplication(codomain(antidomain(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f735,f3263]) ).
fof(f3292,plain,
! [X0] : multiplication(multiplication(codomain(antidomain(X0)),X0),one) = zero,
inference(paramodulation,[status(thm)],[f3264,f42]) ).
fof(f3316,plain,
! [X0] : multiplication(codomain(antidomain(X0)),multiplication(X0,one)) = zero,
inference(forward_demodulation,[status(thm)],[f27,f3292]) ).
fof(f3317,plain,
! [X0] : zero = multiplication(codomain(antidomain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f28,f3316]) ).
fof(f4131,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f108,f285]) ).
fof(f4186,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f29,f4131]) ).
fof(f5242,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),X0),multiplication(one,X0))
| multiplication(one,X0) != multiplication(one,X0) ),
inference(paramodulation,[status(thm)],[f725,f279]) ).
fof(f5299,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),X0),multiplication(one,X0))
| X0 != multiplication(one,X0) ),
inference(forward_demodulation,[status(thm)],[f29,f5242]) ).
fof(f5300,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),X0),multiplication(one,X0))
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f29,f5299]) ).
fof(f5301,plain,
! [X0,X1] :
( leq(multiplication(codomain(X1),X0),X0)
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f29,f5300]) ).
fof(f5302,plain,
! [X0,X1] : leq(multiplication(codomain(X0),X1),X1),
inference(trivial_equality_resolution,[status(thm)],[f5301]) ).
fof(f7465,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f439]) ).
fof(f7850,plain,
! [X0,X1] :
( addition(X1,addition(X1,X0)) = X1
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f7465,f626]) ).
fof(f7891,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(addition(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f7465,f7850]) ).
fof(f25290,plain,
! [X0] : zero = multiplication(codomain(one),multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(paramodulation,[status(thm)],[f2525,f3317]) ).
fof(f25353,plain,
! [X0] : zero = multiplication(one,multiplication(codomain(X0),domain(coantidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f355,f25290]) ).
fof(f25354,plain,
! [X0] : zero = multiplication(codomain(X0),domain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f29,f25353]) ).
fof(f52841,plain,
! [X0] :
( ~ leq(zero,multiplication(codomain(X0),antidomain(coantidomain(X0))))
| codomain(X0) = multiplication(codomain(X0),antidomain(coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f25354,f1395]) ).
fof(f52983,plain,
! [X0] : codomain(X0) = multiplication(codomain(X0),antidomain(coantidomain(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f52841,f118]) ).
fof(f54595,plain,
! [X0] : leq(codomain(X0),antidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f52983,f5302]) ).
fof(f67553,plain,
! [X0] : multiplication(addition(one,antidomain(coantidomain(X0))),codomain(X0)) = addition(codomain(X0),antidomain(coantidomain(X0))),
inference(paramodulation,[status(thm)],[f1728,f265]) ).
fof(f67577,plain,
! [X0] : multiplication(one,codomain(X0)) = addition(codomain(X0),antidomain(coantidomain(X0))),
inference(forward_demodulation,[status(thm)],[f707,f67553]) ).
fof(f67578,plain,
! [X0] : addition(codomain(X0),antidomain(coantidomain(X0))) = codomain(X0),
inference(forward_demodulation,[status(thm)],[f29,f67577]) ).
fof(f67931,plain,
! [X0] :
( addition(codomain(X0),antidomain(coantidomain(X0))) = antidomain(coantidomain(X0))
| ~ leq(codomain(X0),antidomain(coantidomain(X0))) ),
inference(paramodulation,[status(thm)],[f67578,f7891]) ).
fof(f67990,plain,
! [X0] :
( codomain(X0) = antidomain(coantidomain(X0))
| ~ leq(codomain(X0),antidomain(coantidomain(X0))) ),
inference(forward_demodulation,[status(thm)],[f67578,f67931]) ).
fof(f67991,plain,
! [X0] : codomain(X0) = antidomain(coantidomain(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f67990,f54595]) ).
fof(f68069,plain,
! [X0] : codomain(coantidomain(X0)) = antidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f45,f67991]) ).
fof(f68156,plain,
! [X0] : domain(coantidomain(X0)) = antidomain(codomain(X0)),
inference(paramodulation,[status(thm)],[f67991,f41]) ).
fof(f68199,plain,
! [X0] : antidomain(codomain(X0)) = coantidomain(codomain(X0)),
inference(forward_demodulation,[status(thm)],[f115,f68069]) ).
fof(f68331,plain,
coantidomain(sK0_skl) != antidomain(codomain(sK0_skl)),
inference(backward_demodulation,[status(thm)],[f68156,f48]) ).
fof(f68410,plain,
! [X0] : multiplication(antidomain(codomain(X0)),coantidomain(X0)) = coantidomain(X0),
inference(paramodulation,[status(thm)],[f68156,f4186]) ).
fof(f68707,plain,
coantidomain(codomain(sK0_skl)) != coantidomain(sK0_skl),
inference(forward_demodulation,[status(thm)],[f68199,f68331]) ).
fof(f71281,plain,
! [X0] : multiplication(coantidomain(codomain(X0)),coantidomain(X0)) = coantidomain(X0),
inference(forward_demodulation,[status(thm)],[f68199,f68410]) ).
fof(f71316,plain,
! [X0] :
( ~ leq(multiplication(coantidomain(codomain(X0)),codomain(X0)),coantidomain(X0))
| multiplication(coantidomain(codomain(X0)),coantidomain(X0)) = coantidomain(codomain(X0)) ),
inference(paramodulation,[status(thm)],[f71281,f1396]) ).
fof(f71431,plain,
! [X0] :
( ~ leq(multiplication(coantidomain(codomain(X0)),codomain(X0)),coantidomain(X0))
| coantidomain(X0) = coantidomain(codomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f71281,f71316]) ).
fof(f71432,plain,
! [X0] :
( ~ leq(zero,coantidomain(X0))
| coantidomain(X0) = coantidomain(codomain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2516,f71431]) ).
fof(f71433,plain,
! [X0] : coantidomain(codomain(X0)) = coantidomain(X0),
inference(forward_subsumption_resolution,[status(thm)],[f71432,f118]) ).
fof(f71576,plain,
coantidomain(sK0_skl) != coantidomain(sK0_skl),
inference(backward_demodulation,[status(thm)],[f71433,f68707]) ).
fof(f71714,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f71576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 22:42:36 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Drodi V4.1.1
% 46.33/6.24 % Refutation found
% 46.33/6.24 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.33/6.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.93/6.33 % Elapsed time: 6.030116 seconds
% 14.93/6.33 % CPU time: 47.574290 seconds
% 14.93/6.33 % Total memory used: 600.023 MB
% 14.93/6.33 % Net memory used: 580.075 MB
%------------------------------------------------------------------------------