%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:04:36 PM UTC 2026
% Result : Unsatisfiable 18.45s 2.74s
% Output : CNFRefutation 18.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 110 ( 110 unt; 0 def)
% Number of atoms : 110 ( 109 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 270 ( 270 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : sum(additive_identity,X,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,Z,W,Y,V,X] : ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Z,V2,Y,V1,V4,V3] : ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(X,V3,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,V2,Y,V1,V4,V3] : ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(V3,X,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,V,U] : ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,W,Z,Y] : ifeq2(sum(X,W,Z),true,ifeq2(sum(X,Y,Z),true,Y,W),W) = W,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X1,X6),true,product(X0,X6,X5),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X4,X2,X5),true,ifeq(sum(X3,X0,X6),true,product(X6,X1,X5),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X3,X2),true,X3,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f44,plain,
product(a,additive_identity,additive_identity) != true,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,X1,X2),true,ifeq(product(additive_inverse(X0),X1,X3),true,ifeq(sum(X3,X2,X4),true,ifeq(true,true,product(additive_identity,X1,X4),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f39]) ).
fof(f132,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_inverse(X1),X3),true,ifeq(sum(X3,X2,X4),true,ifeq(true,true,product(X0,additive_identity,X4),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f37]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,X1,X2),true,ifeq(product(additive_inverse(X0),X1,X3),true,ifeq(sum(X3,X2,X4),true,product(additive_identity,X1,X4),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f125]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_inverse(X1),X3),true,ifeq(sum(X3,X2,X4),true,product(X0,additive_identity,X4),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f132]) ).
fof(f249,plain,
! [X0,X1,X2] : ifeq2(true,true,ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),multiply(X0,X1)) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f27,f41]) ).
fof(f251,plain,
! [X0,X1,X2] : ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f249]) ).
fof(f466,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f486,plain,
! [X0,X1,X2,X3] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f466]) ).
fof(f1213,plain,
! [X0,X1] : ifeq(true,true,sum(X0,X1,add(X1,X0)),true) = true,
inference(paramodulation,[status(thm)],[f28,f33]) ).
fof(f1227,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)) = true,
inference(forward_demodulation,[status(thm)],[f24,f1213]) ).
fof(f1240,plain,
! [X0,X1] : ifeq2(true,true,ifeq2(sum(X0,additive_identity,X1),true,X1,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f1241,plain,
! [X0,X1,X2] : ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)) = add(X0,X1),
inference(paramodulation,[status(thm)],[f28,f40]) ).
fof(f1244,plain,
! [X0,X1] : ifeq2(sum(X0,additive_inverse(X0),X1),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f30,f40]) ).
fof(f1250,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X1,X0) = X0,
inference(forward_demodulation,[status(thm)],[f23,f1240]) ).
fof(f1251,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f1241]) ).
fof(f1254,plain,
! [X0,X1] : ifeq2(sum(X0,additive_inverse(X0),X1),true,additive_identity,X1) = X1,
inference(forward_demodulation,[status(thm)],[f23,f1244]) ).
fof(f1258,plain,
! [X0,X1] : ifeq2(true,true,ifeq2(sum(additive_inverse(X0),X1,additive_identity),true,X1,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f29,f42]) ).
fof(f1266,plain,
! [X0,X1] : ifeq2(sum(X0,X1,X0),true,ifeq2(true,true,additive_identity,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f26,f42]) ).
fof(f1269,plain,
! [X0,X1] : ifeq2(sum(additive_inverse(X0),X1,additive_identity),true,X1,X0) = X0,
inference(forward_demodulation,[status(thm)],[f23,f1258]) ).
fof(f1277,plain,
! [X0,X1] : ifeq2(sum(X0,X1,X0),true,additive_identity,X1) = X1,
inference(forward_demodulation,[status(thm)],[f23,f1266]) ).
fof(f1344,plain,
ifeq2(true,true,additive_identity,additive_inverse(additive_identity)) = additive_inverse(additive_identity),
inference(paramodulation,[status(thm)],[f30,f1277]) ).
fof(f1348,plain,
additive_identity = additive_inverse(additive_identity),
inference(forward_demodulation,[status(thm)],[f23,f1344]) ).
fof(f1433,plain,
! [X0] : ifeq2(true,true,add(X0,additive_identity),X0) = X0,
inference(paramodulation,[status(thm)],[f28,f1250]) ).
fof(f1439,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(forward_demodulation,[status(thm)],[f23,f1433]) ).
fof(f1593,plain,
! [X0] : ifeq2(true,true,additive_identity,add(X0,additive_inverse(X0))) = add(X0,additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f28,f1254]) ).
fof(f1597,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f23,f1593]) ).
fof(f1608,plain,
! [X0] : ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0) = X0,
inference(paramodulation,[status(thm)],[f30,f1269]) ).
fof(f1612,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f23,f1608]) ).
fof(f1616,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(paramodulation,[status(thm)],[f1612,f1597]) ).
fof(f1969,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(additive_inverse(X0),X1,X3),true,ifeq(true,true,product(additive_identity,X1,add(X3,X2)),true),true),true) = true,
inference(paramodulation,[status(thm)],[f28,f136]) ).
fof(f1978,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(additive_inverse(X0),X1,X3),true,product(additive_identity,X1,add(X3,X2)),true),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f1969]) ).
fof(f2120,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,ifeq(true,true,product(additive_identity,X1,add(multiply(additive_inverse(X0),X1),X2)),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f1978]) ).
fof(f2129,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(additive_identity,X1,add(multiply(additive_inverse(X0),X1),X2)),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f2120]) ).
fof(f2131,plain,
! [X0,X1] : ifeq(true,true,product(additive_identity,X0,add(multiply(additive_inverse(X1),X0),multiply(X1,X0))),true) = true,
inference(paramodulation,[status(thm)],[f27,f2129]) ).
fof(f2153,plain,
! [X0,X1] : product(additive_identity,X0,add(multiply(additive_inverse(X1),X0),multiply(X1,X0))) = true,
inference(forward_demodulation,[status(thm)],[f24,f2131]) ).
fof(f2589,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_inverse(X1),X3),true,ifeq(true,true,product(X0,additive_identity,add(X3,X2)),true),true),true) = true,
inference(paramodulation,[status(thm)],[f28,f140]) ).
fof(f2600,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,additive_inverse(X1),X3),true,product(X0,additive_identity,add(X3,X2)),true),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f2589]) ).
fof(f2642,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,ifeq(true,true,product(X0,additive_identity,add(multiply(X0,additive_inverse(X1)),X2)),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f2600]) ).
fof(f2643,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,additive_inverse(X1),X2),true,ifeq(product(X0,X1,X3),true,product(X0,additive_identity,add(X3,X2)),true),true) = true,
inference(paramodulation,[status(thm)],[f1612,f2600]) ).
fof(f2653,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(X0,additive_identity,add(multiply(X0,additive_inverse(X1)),X2)),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f2642]) ).
fof(f2655,plain,
! [X0,X1] : ifeq(true,true,product(X0,additive_identity,add(multiply(X0,additive_inverse(X1)),multiply(X0,X1))),true) = true,
inference(paramodulation,[status(thm)],[f27,f2653]) ).
fof(f2681,plain,
! [X0,X1] : product(X0,additive_identity,add(multiply(X0,additive_inverse(X1)),multiply(X0,X1))) = true,
inference(forward_demodulation,[status(thm)],[f24,f2655]) ).
fof(f2767,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,X1,X2),true,product(X0,additive_identity,add(X2,multiply(X0,additive_inverse(X1)))),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f2643]) ).
fof(f2784,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(X0,additive_identity,add(X2,multiply(X0,additive_inverse(X1)))),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f2767]) ).
fof(f3679,plain,
! [X0,X1] : ifeq2(true,true,add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),multiply(additive_identity,X1)) = multiply(additive_identity,X1),
inference(paramodulation,[status(thm)],[f2153,f251]) ).
fof(f3991,plain,
! [X0,X1] : add(multiply(additive_inverse(X0),X1),multiply(X0,X1)) = multiply(additive_identity,X1),
inference(forward_demodulation,[status(thm)],[f23,f3679]) ).
fof(f4256,plain,
! [X0] : add(multiply(additive_identity,X0),multiply(additive_identity,X0)) = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f1348,f3991]) ).
fof(f4263,plain,
! [X0,X1] : ifeq(product(X0,X1,multiply(additive_inverse(X0),additive_inverse(X1))),true,product(X0,additive_identity,multiply(additive_identity,additive_inverse(X1))),true) = true,
inference(paramodulation,[status(thm)],[f3991,f2784]) ).
fof(f4910,plain,
! [X0,X1] : ifeq2(true,true,add(X0,X1),add(X1,X0)) = add(X1,X0),
inference(paramodulation,[status(thm)],[f1227,f1251]) ).
fof(f5004,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f23,f4910]) ).
fof(f5106,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,X2,add(X1,X0)) = add(X0,X1),
inference(paramodulation,[status(thm)],[f5004,f1251]) ).
fof(f6688,plain,
! [X0,X1] : ifeq2(true,true,add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)),multiply(X0,additive_identity)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f2681,f251]) ).
fof(f7169,plain,
! [X0,X1] : add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)) = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f23,f6688]) ).
fof(f7440,plain,
! [X0] : add(multiply(X0,additive_identity),multiply(X0,additive_identity)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f1348,f7169]) ).
fof(f8257,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f486]) ).
fof(f8276,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f24,f8257]) ).
fof(f8286,plain,
! [X0,X1] : ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true) = true,
inference(paramodulation,[status(thm)],[f1227,f8276]) ).
fof(f8308,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1) = true,
inference(forward_demodulation,[status(thm)],[f24,f8286]) ).
fof(f8412,plain,
! [X0,X1] : ifeq2(true,true,X0,add(add(X0,X1),additive_inverse(X1))) = add(additive_inverse(X1),add(X0,X1)),
inference(paramodulation,[status(thm)],[f8308,f5106]) ).
fof(f8535,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f8412]) ).
fof(f8833,plain,
! [X0] : multiply(additive_identity,X0) = add(additive_inverse(multiply(additive_identity,X0)),multiply(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f4256,f8535]) ).
fof(f8834,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = add(additive_inverse(multiply(X0,X1)),multiply(additive_identity,X1)),
inference(paramodulation,[status(thm)],[f3991,f8535]) ).
fof(f8835,plain,
! [X0] : multiply(X0,additive_identity) = add(additive_inverse(multiply(X0,additive_identity)),multiply(X0,additive_identity)),
inference(paramodulation,[status(thm)],[f7440,f8535]) ).
fof(f8836,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(additive_inverse(multiply(X0,X1)),multiply(X0,additive_identity)),
inference(paramodulation,[status(thm)],[f7169,f8535]) ).
fof(f8931,plain,
! [X0,X1] : ifeq(product(X0,X1,multiply(additive_inverse(X0),additive_inverse(X1))),true,product(X0,additive_identity,additive_identity),true) = true,
inference(backward_demodulation,[status(thm)],[f9125,f4263]) ).
fof(f9125,plain,
! [X0] : multiply(additive_identity,X0) = additive_identity,
inference(forward_demodulation,[status(thm)],[f1616,f8833]) ).
fof(f9126,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(forward_demodulation,[status(thm)],[f9125,f8834]) ).
fof(f9193,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1439,f9126]) ).
fof(f9385,plain,
! [X0] : multiply(X0,additive_identity) = additive_identity,
inference(forward_demodulation,[status(thm)],[f1616,f8835]) ).
fof(f9386,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(multiply(additive_inverse(X0),X1),multiply(X0,additive_identity)),
inference(forward_demodulation,[status(thm)],[f9193,f8836]) ).
fof(f9387,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(multiply(additive_inverse(X0),X1),additive_identity),
inference(forward_demodulation,[status(thm)],[f9385,f9386]) ).
fof(f9404,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = multiply(additive_inverse(X0),X1),
inference(forward_demodulation,[status(thm)],[f1439,f9387]) ).
fof(f9417,plain,
! [X0,X1] : ifeq(product(X0,X1,multiply(X0,additive_inverse(additive_inverse(X1)))),true,product(X0,additive_identity,additive_identity),true) = true,
inference(forward_demodulation,[status(thm)],[f9404,f8931]) ).
fof(f9418,plain,
! [X0,X1] : ifeq(product(X0,X1,multiply(X0,X1)),true,product(X0,additive_identity,additive_identity),true) = true,
inference(forward_demodulation,[status(thm)],[f1612,f9417]) ).
fof(f9419,plain,
! [X0] : ifeq(true,true,product(X0,additive_identity,additive_identity),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f9418]) ).
fof(f9420,plain,
true != true,
inference(backward_demodulation,[status(thm)],[f9427,f44]) ).
fof(f9427,plain,
! [X0] : product(X0,additive_identity,additive_identity) = true,
inference(forward_demodulation,[status(thm)],[f24,f9419]) ).
fof(f10042,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f9420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:09:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 18.45/2.74 % Refutation found
% 18.45/2.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 18.45/2.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.59/3.22 % Elapsed time: 2.853555 seconds
% 1.59/3.22 % CPU time: 20.219712 seconds
% 1.59/3.22 % Total memory used: 345.785 MB
% 1.59/3.22 % Net memory used: 328.640 MB
%------------------------------------------------------------------------------