%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE080+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 : n007.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 12:57:55 PM UTC 2026
% Result : Theorem 43.81s 16.12s
% Output : CNFRefutation 44.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 161 ( 156 unt; 0 def)
% Number of atoms : 171 ( 170 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 248 ( 246 !; 2 ?)
% 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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> antidomain(antidomain(X0)) = domain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> antidomain(antidomain(X0)) = 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(f22,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
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(f38,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
? [X0] :
( antidomain(antidomain(X0)) != domain(X0)
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( ? [X0] : antidomain(antidomain(X0)) != domain(X0)
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ! [X1] : addition(domain(X1),antidomain(X1)) = one ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( antidomain(antidomain(sK0_skl)) != domain(sK0_skl)
& ! [X1] : multiplication(domain(X1),antidomain(X1)) = zero
& ! [X1] : addition(domain(X1),antidomain(X1)) = one ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f41]) ).
fof(f43,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
antidomain(antidomain(sK0_skl)) != domain(sK0_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f59,plain,
addition(zero,antidomain(zero)) = one,
inference(paramodulation,[status(thm)],[f38,f43]) ).
fof(f60,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f48,f59]) ).
fof(f78,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(paramodulation,[status(thm)],[f20,f37]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f114,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f96]) ).
fof(f139,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f114]) ).
fof(f194,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = addition(zero,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f44,f27]) ).
fof(f200,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = addition(multiplication(domain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f44,f27]) ).
fof(f202,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f217,plain,
! [X0,X1] : multiplication(domain(X0),addition(antidomain(X0),X1)) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f48,f194]) ).
fof(f225,plain,
! [X0,X1] : multiplication(domain(X0),addition(X1,antidomain(X0))) = multiplication(domain(X0),X1),
inference(forward_demodulation,[status(thm)],[f22,f200]) ).
fof(f234,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f20,f28]) ).
fof(f240,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f243,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)],[f24,f28]) ).
fof(f245,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f257,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f28,f234]) ).
fof(f260,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f48,f240]) ).
fof(f677,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X1),domain(X0)),
inference(paramodulation,[status(thm)],[f20,f39]) ).
fof(f682,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),antidomain(X0)) = multiplication(domain(X1),antidomain(X0)),
inference(paramodulation,[status(thm)],[f39,f260]) ).
fof(f683,plain,
! [X0,X1,X2] : addition(domain(X0),addition(domain(X1),X2)) = addition(domain(addition(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f39,f21]) ).
fof(f687,plain,
! [X0,X1] : domain(addition(X0,X1)) = domain(addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f39,f677]) ).
fof(f1006,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f1023,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f1006]) ).
fof(f1043,plain,
! [X0,X1] : domain(addition(X0,domain(X1))) = addition(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f1023,f39]) ).
fof(f1044,plain,
! [X0,X1] : domain(addition(domain(X0),X1)) = addition(domain(X0),domain(X1)),
inference(paramodulation,[status(thm)],[f1023,f39]) ).
fof(f1048,plain,
! [X0] : addition(domain(X0),antidomain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f1023,f43]) ).
fof(f1053,plain,
! [X0,X1] : domain(addition(X0,domain(X1))) = domain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f39,f1043]) ).
fof(f1054,plain,
! [X0,X1] : domain(addition(domain(X0),X1)) = domain(addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f39,f1044]) ).
fof(f1059,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f1061,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) = multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f36,f35]) ).
fof(f1073,plain,
! [X0] : addition(multiplication(domain(X0),X0),multiplication(domain(X0),X0)) = addition(multiplication(domain(X0),X0),X0),
inference(paramodulation,[status(thm)],[f35,f114]) ).
fof(f1078,plain,
one = multiplication(domain(one),one),
inference(forward_demodulation,[status(thm)],[f78,f1059]) ).
fof(f1079,plain,
one = domain(one),
inference(forward_demodulation,[status(thm)],[f25,f1078]) ).
fof(f1081,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)) = multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f243,f1061]) ).
fof(f1082,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f36,f1081]) ).
fof(f1088,plain,
! [X0] : multiplication(domain(X0),addition(X0,X0)) = addition(multiplication(domain(X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f27,f1073]) ).
fof(f1090,plain,
! [X0] : multiplication(domain(X0),X0) = addition(multiplication(domain(X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f23,f1088]) ).
fof(f1247,plain,
! [X0] : multiplication(one,antidomain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f1048,f260]) ).
fof(f1262,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f1247]) ).
fof(f1290,plain,
! [X0] : addition(antidomain(X0),one) = addition(domain(X0),antidomain(X0)),
inference(paramodulation,[status(thm)],[f20,f139]) ).
fof(f1299,plain,
! [X0] : domain(addition(domain(X0),antidomain(X0))) = domain(addition(antidomain(X0),one)),
inference(paramodulation,[status(thm)],[f139,f687]) ).
fof(f1317,plain,
! [X0] : addition(antidomain(X0),one) = one,
inference(forward_demodulation,[status(thm)],[f43,f1290]) ).
fof(f1330,plain,
! [X0] : domain(addition(X0,antidomain(X0))) = domain(addition(antidomain(X0),one)),
inference(forward_demodulation,[status(thm)],[f1054,f1299]) ).
fof(f1331,plain,
! [X0] : domain(addition(X0,antidomain(X0))) = domain(one),
inference(forward_demodulation,[status(thm)],[f1317,f1330]) ).
fof(f1332,plain,
! [X0] : domain(addition(X0,antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f1079,f1331]) ).
fof(f1457,plain,
! [X0] : domain(addition(X0,one)) = addition(domain(X0),one),
inference(paramodulation,[status(thm)],[f1079,f39]) ).
fof(f1481,plain,
! [X0] : domain(addition(X0,one)) = one,
inference(forward_demodulation,[status(thm)],[f37,f1457]) ).
fof(f1549,plain,
! [X0,X1] : domain(multiplication(X0,addition(X1,one))) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f1481,f36]) ).
fof(f1580,plain,
! [X0,X1] : domain(multiplication(X0,addition(X1,one))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f25,f1549]) ).
fof(f1788,plain,
! [X0,X1] : domain(multiplication(X0,addition(X1,antidomain(X1)))) = domain(multiplication(X0,one)),
inference(paramodulation,[status(thm)],[f1332,f36]) ).
fof(f1793,plain,
! [X0,X1] : domain(addition(X0,addition(X1,antidomain(X1)))) = addition(domain(X0),one),
inference(paramodulation,[status(thm)],[f1332,f39]) ).
fof(f1822,plain,
! [X0,X1] : domain(multiplication(X0,addition(X1,antidomain(X1)))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f25,f1788]) ).
fof(f1829,plain,
! [X0,X1] : domain(addition(X0,addition(X1,antidomain(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f37,f1793]) ).
fof(f2556,plain,
! [X0] : domain(addition(antidomain(X0),X0)) = one,
inference(paramodulation,[status(thm)],[f114,f1829]) ).
fof(f4947,plain,
! [X0] : domain(multiplication(domain(X0),antidomain(antidomain(X0)))) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f217,f1822]) ).
fof(f4999,plain,
! [X0] : domain(multiplication(domain(X0),antidomain(antidomain(X0)))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f1023,f4947]) ).
fof(f7438,plain,
! [X0,X1] : multiplication(one,X0) = addition(multiplication(antidomain(X1),X0),X0),
inference(paramodulation,[status(thm)],[f1317,f245]) ).
fof(f7441,plain,
! [X0,X1] : multiplication(one,X0) = addition(multiplication(domain(X1),X0),X0),
inference(paramodulation,[status(thm)],[f37,f245]) ).
fof(f7532,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(multiplication(addition(X1,one),X0),X2),
inference(paramodulation,[status(thm)],[f245,f257]) ).
fof(f7548,plain,
! [X0,X1] : X0 = addition(multiplication(antidomain(X1),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f7438]) ).
fof(f7551,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f7552,f1090]) ).
fof(f7552,plain,
! [X0,X1] : X0 = addition(multiplication(domain(X1),X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f7441]) ).
fof(f7616,plain,
! [X0,X1] : multiplication(addition(domain(multiplication(X0,X1)),one),multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(backward_demodulation,[status(thm)],[f7618,f1082]) ).
fof(f7618,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(X1,one),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f24,f7532]) ).
fof(f7659,plain,
! [X0,X1] : multiplication(one,multiplication(X0,domain(X1))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f37,f7616]) ).
fof(f7660,plain,
! [X0,X1] : multiplication(X0,domain(X1)) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f26,f7659]) ).
fof(f7724,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(X0,X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f7551,f24]) ).
fof(f8359,plain,
! [X0,X1] : multiplication(domain(X0),antidomain(X0)) = multiplication(domain(X0),multiplication(antidomain(X1),antidomain(X0))),
inference(paramodulation,[status(thm)],[f7548,f225]) ).
fof(f8470,plain,
! [X0,X1] : zero = multiplication(domain(X0),multiplication(antidomain(X1),antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f44,f8359]) ).
fof(f9553,plain,
! [X0,X1] : multiplication(X0,one) = addition(multiplication(X0,antidomain(X1)),X0),
inference(paramodulation,[status(thm)],[f1317,f202]) ).
fof(f9639,plain,
! [X0,X1] : domain(multiplication(domain(X0),addition(X1,one))) = domain(addition(multiplication(domain(X0),X1),X0)),
inference(paramodulation,[status(thm)],[f202,f1053]) ).
fof(f9677,plain,
! [X0,X1] : domain(addition(X0,multiplication(X0,X1))) = domain(multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f202,f687]) ).
fof(f9691,plain,
! [X0,X1] : X0 = addition(multiplication(X0,antidomain(X1)),X0),
inference(forward_demodulation,[status(thm)],[f25,f9553]) ).
fof(f9793,plain,
! [X0,X1] : domain(domain(X0)) = domain(addition(multiplication(domain(X0),X1),X0)),
inference(forward_demodulation,[status(thm)],[f1580,f9639]) ).
fof(f9794,plain,
! [X0,X1] : domain(X0) = domain(addition(multiplication(domain(X0),X1),X0)),
inference(forward_demodulation,[status(thm)],[f1023,f9793]) ).
fof(f9807,plain,
! [X0,X1] : domain(addition(X0,multiplication(X0,X1))) = domain(X0),
inference(forward_demodulation,[status(thm)],[f1580,f9677]) ).
fof(f9826,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f20,f9691]) ).
fof(f9828,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(X0),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f1262,f9691]) ).
fof(f11871,plain,
! [X0,X1] : addition(domain(X0),one) = addition(domain(addition(X0,X1)),antidomain(X1)),
inference(paramodulation,[status(thm)],[f43,f683]) ).
fof(f12057,plain,
! [X0,X1] : one = addition(domain(addition(X0,X1)),antidomain(X1)),
inference(forward_demodulation,[status(thm)],[f37,f11871]) ).
fof(f12197,plain,
! [X0,X1] : one = addition(antidomain(X0),domain(addition(X1,X0))),
inference(paramodulation,[status(thm)],[f20,f12057]) ).
fof(f12207,plain,
! [X0,X1] : one = addition(domain(X0),antidomain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f9807,f12057]) ).
fof(f12394,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f9794,f12197]) ).
fof(f12902,plain,
! [X0,X1] : multiplication(one,antidomain(X0)) = multiplication(antidomain(multiplication(X0,X1)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f12207,f260]) ).
fof(f12958,plain,
! [X0,X1] : antidomain(X0) = multiplication(antidomain(multiplication(X0,X1)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f12902]) ).
fof(f15032,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(X0),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f7551,f12958]) ).
fof(f26444,plain,
! [X0] : zero = multiplication(antidomain(X0),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f7724,f8470]) ).
fof(f26797,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(domain(zero),multiplication(domain(X0),domain(antidomain(X0)))),
inference(paramodulation,[status(thm)],[f44,f7660]) ).
fof(f26957,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = multiplication(zero,multiplication(domain(X0),domain(antidomain(X0)))),
inference(forward_demodulation,[status(thm)],[f38,f26797]) ).
fof(f26959,plain,
! [X0] : multiplication(domain(X0),domain(antidomain(X0))) = zero,
inference(forward_demodulation,[status(thm)],[f30,f26957]) ).
fof(f27730,plain,
! [X0] : multiplication(antidomain(X0),domain(antidomain(antidomain(X0)))) = multiplication(domain(zero),multiplication(antidomain(X0),domain(antidomain(antidomain(X0))))),
inference(paramodulation,[status(thm)],[f26444,f7660]) ).
fof(f27794,plain,
! [X0] : multiplication(antidomain(X0),domain(antidomain(antidomain(X0)))) = multiplication(zero,multiplication(antidomain(X0),domain(antidomain(antidomain(X0))))),
inference(forward_demodulation,[status(thm)],[f38,f27730]) ).
fof(f27795,plain,
! [X0] : multiplication(antidomain(X0),domain(antidomain(antidomain(X0)))) = zero,
inference(forward_demodulation,[status(thm)],[f30,f27794]) ).
fof(f42346,plain,
! [X0] : antidomain(X0) = addition(antidomain(X0),antidomain(domain(X0))),
inference(paramodulation,[status(thm)],[f15032,f9826]) ).
fof(f43105,plain,
! [X0] : antidomain(X0) = antidomain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f9828,f42346]) ).
fof(f43431,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(domain(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f43105]) ).
fof(f43668,plain,
! [X0,X1] : antidomain(multiplication(X0,domain(X1))) = antidomain(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f43105,f43431]) ).
fof(f50478,plain,
! [X0] : multiplication(one,antidomain(antidomain(X0))) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(paramodulation,[status(thm)],[f2556,f682]) ).
fof(f50690,plain,
! [X0] : domain(antidomain(antidomain(X0))) = domain(X0),
inference(backward_demodulation,[status(thm)],[f50708,f4999]) ).
fof(f50708,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(domain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[status(thm)],[f26,f50478]) ).
fof(f51002,plain,
! [X0] : multiplication(antidomain(X0),domain(X0)) = zero,
inference(backward_demodulation,[status(thm)],[f50690,f27795]) ).
fof(f51057,plain,
! [X0] : multiplication(domain(antidomain(X0)),domain(X0)) = zero,
inference(paramodulation,[status(thm)],[f50690,f26959]) ).
fof(f51609,plain,
! [X0] : domain(multiplication(antidomain(X0),X0)) = domain(zero),
inference(paramodulation,[status(thm)],[f51002,f36]) ).
fof(f51716,plain,
! [X0] : domain(multiplication(antidomain(X0),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f38,f51609]) ).
fof(f52194,plain,
! [X0] : multiplication(zero,multiplication(antidomain(X0),X0)) = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f51716,f7551]) ).
fof(f52386,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(forward_demodulation,[status(thm)],[f30,f52194]) ).
fof(f52553,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f52386,f27]) ).
fof(f52646,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f22,f52553]) ).
fof(f54245,plain,
! [X0] : antidomain(zero) = antidomain(multiplication(domain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f51057,f43668]) ).
fof(f54394,plain,
! [X0] : one = antidomain(multiplication(domain(antidomain(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f60,f54245]) ).
fof(f54533,plain,
! [X0] : zero = multiplication(one,multiplication(domain(antidomain(X0)),X0)),
inference(paramodulation,[status(thm)],[f54394,f52386]) ).
fof(f54713,plain,
! [X0] : zero = multiplication(domain(antidomain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f26,f54533]) ).
fof(f54958,plain,
! [X0,X1] : multiplication(addition(X0,domain(antidomain(X1))),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f54713,f28]) ).
fof(f55113,plain,
! [X0,X1] : multiplication(addition(X0,domain(antidomain(X1))),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f54958]) ).
fof(f81436,plain,
! [X0] : multiplication(antidomain(antidomain(X0)),one) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f52646]) ).
fof(f81690,plain,
! [X0] : antidomain(antidomain(X0)) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(forward_demodulation,[status(thm)],[f25,f81436]) ).
fof(f84304,plain,
! [X0] : multiplication(one,X0) = multiplication(antidomain(antidomain(X0)),X0),
inference(paramodulation,[status(thm)],[f12394,f55113]) ).
fof(f84506,plain,
! [X0] : X0 = multiplication(antidomain(antidomain(X0)),X0),
inference(forward_demodulation,[status(thm)],[f26,f84304]) ).
fof(f84756,plain,
! [X0] : domain(X0) = multiplication(antidomain(antidomain(X0)),domain(X0)),
inference(paramodulation,[status(thm)],[f43105,f84506]) ).
fof(f84910,plain,
domain(sK0_skl) != domain(sK0_skl),
inference(backward_demodulation,[status(thm)],[f85061,f45]) ).
fof(f85061,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f81690,f84756]) ).
fof(f85516,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f84910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE080+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.41 % Computer : n007.cluster.edu
% 0.15/10.41 % Model : x86_64 x86_64
% 0.15/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.41 % Memory : 8046.5625MB
% 0.15/10.41 % OS : Linux 6.8.0-71-generic
% 0.15/10.41 % CPULimit : 300
% 0.15/10.41 % WCLimit : 300
% 0.15/10.41 % DateTime : Sun Sep 20 22:40:31 UTC 2026
% 0.15/10.41 % CPUTime :
% 0.15/10.42 % Drodi V4.1.1
% 43.81/16.12 % Refutation found
% 43.81/16.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 43.81/16.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.80/16.24 % Elapsed time: 5.808299 seconds
% 7.80/16.24 % CPU time: 45.394551 seconds
% 7.80/16.24 % Total memory used: 310.916 MB
% 7.80/16.24 % Net memory used: 303.744 MB
%------------------------------------------------------------------------------