TSTP Solution File: RNG027-9 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : RNG027-9 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 14:06:56 EDT 2024
% Result : Unsatisfiable 2.78s 0.89s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 15
% Syntax : Number of formulae : 183 ( 183 unt; 0 def)
% Number of atoms : 183 ( 182 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 24 ( 24 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 489 ( 489 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9223,plain,
$false,
inference(subsumption_resolution,[],[f9222,f7492]) ).
fof(f7492,plain,
! [X2,X3,X0,X1] : add(additive_inverse(associator(X1,X2,X0)),add(X3,associator(X0,X1,X2))) = X3,
inference(superposition,[],[f84,f5316]) ).
fof(f5316,plain,
! [X2,X0,X1] : additive_inverse(associator(X0,X2,X1)) = additive_inverse(associator(X2,X1,X0)),
inference(superposition,[],[f5253,f4832]) ).
fof(f4832,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X0,X2,X1)),
inference(forward_demodulation,[],[f4746,f2]) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4746,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(additive_inverse(associator(X0,X2,X1)),additive_identity),
inference(superposition,[],[f84,f4711]) ).
fof(f4711,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X2,X1),associator(X0,X1,X2)),
inference(forward_demodulation,[],[f4710,f1]) ).
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4710,plain,
! [X2,X0,X1] : additive_identity = add(additive_identity,add(associator(X0,X2,X1),associator(X0,X1,X2))),
inference(forward_demodulation,[],[f4709,f2014]) ).
fof(f2014,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X1),
inference(forward_demodulation,[],[f1952,f34]) ).
fof(f34,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(superposition,[],[f6,f7]) ).
fof(f7,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f6,axiom,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1952,plain,
! [X0,X1] : associator(X0,X1,X1) = add(additive_inverse(multiply(X0,multiply(X1,X1))),multiply(X0,multiply(X1,X1))),
inference(superposition,[],[f24,f12]) ).
fof(f12,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f24,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(additive_inverse(multiply(X0,multiply(X1,X2))),multiply(multiply(X0,X1),X2)),
inference(backward_demodulation,[],[f14,f10]) ).
fof(f10,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f14,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4709,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,X1),add(associator(X0,X2,X1),associator(X0,X1,X2))),
inference(forward_demodulation,[],[f4708,f11]) ).
fof(f11,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4708,plain,
! [X2,X0,X1] : additive_identity = add(add(associator(X0,X1,X1),associator(X0,X2,X1)),associator(X0,X1,X2)),
inference(forward_demodulation,[],[f4707,f2049]) ).
fof(f2049,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(associator(X3,X0,X2),associator(X3,X1,X2)),
inference(forward_demodulation,[],[f2048,f420]) ).
fof(f420,plain,
! [X2,X0,X1] : add(X2,X1) = add(additive_inverse(X0),add(X2,add(X0,X1))),
inference(superposition,[],[f303,f328]) ).
fof(f328,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(superposition,[],[f66,f75]) ).
fof(f75,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[],[f70,f10]) ).
fof(f70,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f59,f1]) ).
fof(f59,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f11,f6]) ).
fof(f66,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f11,f10]) ).
fof(f303,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[],[f60,f11]) ).
fof(f60,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X1,X0),X2),
inference(superposition,[],[f11,f10]) ).
fof(f2048,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,multiply(X1,X2))),add(associator(X3,X0,X2),add(multiply(X3,multiply(X1,X2)),associator(X3,X1,X2)))),
inference(forward_demodulation,[],[f2047,f1955]) ).
fof(f1955,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)),
inference(superposition,[],[f70,f24]) ).
fof(f2047,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,multiply(X1,X2))),add(associator(X3,X0,X2),multiply(multiply(X3,X1),X2))),
inference(forward_demodulation,[],[f2046,f328]) ).
fof(f2046,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,multiply(X1,X2))),add(additive_inverse(multiply(X3,multiply(X0,X2))),add(multiply(X3,multiply(X0,X2)),add(associator(X3,X0,X2),multiply(multiply(X3,X1),X2))))),
inference(forward_demodulation,[],[f2022,f11]) ).
fof(f2022,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,multiply(X1,X2))),add(additive_inverse(multiply(X3,multiply(X0,X2))),add(add(multiply(X3,multiply(X0,X2)),associator(X3,X0,X2)),multiply(multiply(X3,X1),X2)))),
inference(backward_demodulation,[],[f1995,f1955]) ).
fof(f1995,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,multiply(X1,X2))),add(additive_inverse(multiply(X3,multiply(X0,X2))),add(multiply(multiply(X3,X0),X2),multiply(multiply(X3,X1),X2)))),
inference(forward_demodulation,[],[f1994,f11]) ).
fof(f1994,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(add(additive_inverse(multiply(X3,multiply(X1,X2))),additive_inverse(multiply(X3,multiply(X0,X2)))),add(multiply(multiply(X3,X0),X2),multiply(multiply(X3,X1),X2))),
inference(forward_demodulation,[],[f1993,f163]) ).
fof(f163,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(superposition,[],[f113,f73]) ).
fof(f73,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(superposition,[],[f70,f7]) ).
fof(f113,plain,
! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
inference(superposition,[],[f84,f84]) ).
fof(f1993,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(add(multiply(X3,multiply(X0,X2)),multiply(X3,multiply(X1,X2)))),add(multiply(multiply(X3,X0),X2),multiply(multiply(X3,X1),X2))),
inference(forward_demodulation,[],[f1992,f8]) ).
fof(f8,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1992,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,add(multiply(X0,X2),multiply(X1,X2)))),add(multiply(multiply(X3,X0),X2),multiply(multiply(X3,X1),X2))),
inference(forward_demodulation,[],[f1991,f9]) ).
fof(f9,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1991,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,add(multiply(X0,X2),multiply(X1,X2)))),multiply(add(multiply(X3,X0),multiply(X3,X1)),X2)),
inference(forward_demodulation,[],[f1942,f8]) ).
fof(f1942,plain,
! [X2,X3,X0,X1] : associator(X3,add(X0,X1),X2) = add(additive_inverse(multiply(X3,add(multiply(X0,X2),multiply(X1,X2)))),multiply(multiply(X3,add(X0,X1)),X2)),
inference(superposition,[],[f24,f9]) ).
fof(f4707,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,add(X1,X2),X1),associator(X0,X1,X2)),
inference(forward_demodulation,[],[f4706,f2]) ).
fof(f4706,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,add(X1,X2),X1),add(associator(X0,X1,X2),additive_identity)),
inference(forward_demodulation,[],[f4705,f2014]) ).
fof(f4705,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,add(X1,X2),X1),add(associator(X0,X1,X2),associator(X0,X2,X2))),
inference(forward_demodulation,[],[f4597,f2049]) ).
fof(f4597,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,add(X1,X2),X1),associator(X0,add(X1,X2),X2)),
inference(superposition,[],[f2045,f2014]) ).
fof(f2045,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(associator(X3,X0,X1),associator(X3,X0,X2)),
inference(forward_demodulation,[],[f2044,f420]) ).
fof(f2044,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,multiply(X0,X2))),add(associator(X3,X0,X1),add(multiply(X3,multiply(X0,X2)),associator(X3,X0,X2)))),
inference(forward_demodulation,[],[f2043,f1955]) ).
fof(f2043,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,multiply(X0,X2))),add(associator(X3,X0,X1),multiply(multiply(X3,X0),X2))),
inference(forward_demodulation,[],[f2042,f328]) ).
fof(f2042,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,multiply(X0,X2))),add(additive_inverse(multiply(X3,multiply(X0,X1))),add(multiply(X3,multiply(X0,X1)),add(associator(X3,X0,X1),multiply(multiply(X3,X0),X2))))),
inference(forward_demodulation,[],[f2021,f11]) ).
fof(f2021,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,multiply(X0,X2))),add(additive_inverse(multiply(X3,multiply(X0,X1))),add(add(multiply(X3,multiply(X0,X1)),associator(X3,X0,X1)),multiply(multiply(X3,X0),X2)))),
inference(backward_demodulation,[],[f1986,f1955]) ).
fof(f1986,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,multiply(X0,X2))),add(additive_inverse(multiply(X3,multiply(X0,X1))),add(multiply(multiply(X3,X0),X1),multiply(multiply(X3,X0),X2)))),
inference(forward_demodulation,[],[f1985,f11]) ).
fof(f1985,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(add(additive_inverse(multiply(X3,multiply(X0,X2))),additive_inverse(multiply(X3,multiply(X0,X1)))),add(multiply(multiply(X3,X0),X1),multiply(multiply(X3,X0),X2))),
inference(forward_demodulation,[],[f1984,f163]) ).
fof(f1984,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(add(multiply(X3,multiply(X0,X1)),multiply(X3,multiply(X0,X2)))),add(multiply(multiply(X3,X0),X1),multiply(multiply(X3,X0),X2))),
inference(forward_demodulation,[],[f1983,f8]) ).
fof(f1983,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,add(multiply(X0,X1),multiply(X0,X2)))),add(multiply(multiply(X3,X0),X1),multiply(multiply(X3,X0),X2))),
inference(forward_demodulation,[],[f1940,f8]) ).
fof(f1940,plain,
! [X2,X3,X0,X1] : associator(X3,X0,add(X1,X2)) = add(additive_inverse(multiply(X3,add(multiply(X0,X1),multiply(X0,X2)))),multiply(multiply(X3,X0),add(X1,X2))),
inference(superposition,[],[f24,f8]) ).
fof(f5253,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X2,X1,X0)),
inference(forward_demodulation,[],[f5185,f2]) ).
fof(f5185,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(additive_inverse(associator(X2,X1,X0)),additive_identity),
inference(superposition,[],[f84,f4893]) ).
fof(f4893,plain,
! [X2,X0,X1] : additive_identity = add(associator(X1,X2,X0),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f4892,f1]) ).
fof(f4892,plain,
! [X2,X0,X1] : additive_identity = add(additive_identity,add(associator(X1,X2,X0),associator(X0,X2,X1))),
inference(forward_demodulation,[],[f4891,f4779]) ).
fof(f4779,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X0),
inference(forward_demodulation,[],[f4722,f1]) ).
fof(f4722,plain,
! [X0,X1] : additive_identity = add(additive_identity,associator(X0,X1,X0)),
inference(superposition,[],[f4711,f2015]) ).
fof(f2015,plain,
! [X0,X1] : additive_identity = associator(X0,X0,X1),
inference(forward_demodulation,[],[f1953,f34]) ).
fof(f1953,plain,
! [X0,X1] : associator(X0,X0,X1) = add(additive_inverse(multiply(X0,multiply(X0,X1))),multiply(X0,multiply(X0,X1))),
inference(superposition,[],[f24,f13]) ).
fof(f13,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f4891,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X2,X0),add(associator(X1,X2,X0),associator(X0,X2,X1))),
inference(forward_demodulation,[],[f4890,f11]) ).
fof(f4890,plain,
! [X2,X0,X1] : additive_identity = add(add(associator(X0,X2,X0),associator(X1,X2,X0)),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f4889,f2053]) ).
fof(f2053,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(associator(X0,X2,X3),associator(X1,X2,X3)),
inference(forward_demodulation,[],[f2052,f420]) ).
fof(f2052,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),add(associator(X0,X2,X3),add(multiply(X1,multiply(X2,X3)),associator(X1,X2,X3)))),
inference(forward_demodulation,[],[f2051,f1955]) ).
fof(f2051,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),add(associator(X0,X2,X3),multiply(multiply(X1,X2),X3))),
inference(forward_demodulation,[],[f2050,f328]) ).
fof(f2050,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),add(additive_inverse(multiply(X0,multiply(X2,X3))),add(multiply(X0,multiply(X2,X3)),add(associator(X0,X2,X3),multiply(multiply(X1,X2),X3))))),
inference(forward_demodulation,[],[f2023,f11]) ).
fof(f2023,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),add(additive_inverse(multiply(X0,multiply(X2,X3))),add(add(multiply(X0,multiply(X2,X3)),associator(X0,X2,X3)),multiply(multiply(X1,X2),X3)))),
inference(backward_demodulation,[],[f2008,f1955]) ).
fof(f2008,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(multiply(X1,multiply(X2,X3))),add(additive_inverse(multiply(X0,multiply(X2,X3))),add(multiply(multiply(X0,X2),X3),multiply(multiply(X1,X2),X3)))),
inference(forward_demodulation,[],[f2007,f11]) ).
fof(f2007,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(add(additive_inverse(multiply(X1,multiply(X2,X3))),additive_inverse(multiply(X0,multiply(X2,X3)))),add(multiply(multiply(X0,X2),X3),multiply(multiply(X1,X2),X3))),
inference(forward_demodulation,[],[f2006,f163]) ).
fof(f2006,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(add(multiply(X0,multiply(X2,X3)),multiply(X1,multiply(X2,X3)))),add(multiply(multiply(X0,X2),X3),multiply(multiply(X1,X2),X3))),
inference(forward_demodulation,[],[f2005,f9]) ).
fof(f2005,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(add(multiply(X0,multiply(X2,X3)),multiply(X1,multiply(X2,X3)))),multiply(add(multiply(X0,X2),multiply(X1,X2)),X3)),
inference(forward_demodulation,[],[f1947,f9]) ).
fof(f1947,plain,
! [X2,X3,X0,X1] : associator(add(X0,X1),X2,X3) = add(additive_inverse(add(multiply(X0,multiply(X2,X3)),multiply(X1,multiply(X2,X3)))),multiply(multiply(add(X0,X1),X2),X3)),
inference(superposition,[],[f24,f9]) ).
fof(f4889,plain,
! [X2,X0,X1] : additive_identity = add(associator(add(X0,X1),X2,X0),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f4888,f2]) ).
fof(f4888,plain,
! [X2,X0,X1] : additive_identity = add(associator(add(X0,X1),X2,X0),add(associator(X0,X2,X1),additive_identity)),
inference(forward_demodulation,[],[f4887,f4779]) ).
fof(f4887,plain,
! [X2,X0,X1] : additive_identity = add(associator(add(X0,X1),X2,X0),add(associator(X0,X2,X1),associator(X1,X2,X1))),
inference(forward_demodulation,[],[f4884,f2053]) ).
fof(f4884,plain,
! [X2,X0,X1] : additive_identity = add(associator(add(X0,X1),X2,X0),associator(add(X0,X1),X2,X1)),
inference(superposition,[],[f4779,f2045]) ).
fof(f84,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(superposition,[],[f73,f10]) ).
fof(f9222,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(additive_inverse(associator(x,z,multiply(x,y))),associator(multiply(x,y),x,z))),
inference(forward_demodulation,[],[f9183,f7498]) ).
fof(f7498,plain,
! [X2,X3,X0,X1,X4] : add(X3,X4) = add(additive_inverse(associator(X1,X2,X0)),add(X3,add(X4,associator(X0,X1,X2)))),
inference(superposition,[],[f419,f5316]) ).
fof(f419,plain,
! [X2,X0,X1] : add(X2,X1) = add(additive_inverse(X0),add(X2,add(X1,X0))),
inference(superposition,[],[f303,f84]) ).
fof(f9183,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(additive_inverse(associator(multiply(x,x),y,z)),add(additive_inverse(associator(x,z,multiply(x,y))),add(associator(multiply(x,y),x,z),associator(z,multiply(x,x),y))))),
inference(backward_demodulation,[],[f8149,f9178]) ).
fof(f9178,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(multiply(X1,X2),X1,X0),associator(X0,multiply(X1,X1),X2)),
inference(forward_demodulation,[],[f8995,f7]) ).
fof(f8995,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(additive_inverse(additive_inverse(associator(multiply(X1,X2),X1,X0))),associator(X0,multiply(X1,X1),X2)),
inference(superposition,[],[f5383,f5253]) ).
fof(f5383,plain,
! [X2,X0,X1] : add(additive_inverse(associator(X0,X1,multiply(X1,X2))),associator(X0,multiply(X1,X1),X2)) = associator(X1,X2,multiply(X0,X1)),
inference(backward_demodulation,[],[f2077,f5382]) ).
fof(f5382,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = associator(X2,X1,X0),
inference(forward_demodulation,[],[f5381,f7]) ).
fof(f5381,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = additive_inverse(additive_inverse(associator(X2,X1,X0))),
inference(forward_demodulation,[],[f5319,f2040]) ).
fof(f2040,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = additive_inverse(associator(X0,X1,X2)),
inference(backward_demodulation,[],[f2013,f2039]) ).
fof(f2039,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = additive_inverse(associator(X2,X0,X1)),
inference(forward_demodulation,[],[f2038,f75]) ).
fof(f2038,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(X2,multiply(X0,X1)),add(additive_inverse(associator(X2,X0,X1)),additive_inverse(multiply(X2,multiply(X0,X1))))),
inference(forward_demodulation,[],[f2020,f163]) ).
fof(f2020,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(X2,multiply(X0,X1)),additive_inverse(add(multiply(X2,multiply(X0,X1)),associator(X2,X0,X1)))),
inference(backward_demodulation,[],[f1982,f1955]) ).
fof(f1982,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(multiply(X2,multiply(X0,X1)),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1981,f7]) ).
fof(f1981,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(additive_inverse(additive_inverse(multiply(X2,multiply(X0,X1)))),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1980,f18]) ).
fof(f18,axiom,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1980,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1)))),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1939,f18]) ).
fof(f1939,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = add(additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1)))),multiply(multiply(X2,X0),additive_inverse(X1))),
inference(superposition,[],[f24,f18]) ).
fof(f2013,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = associator(X0,X1,additive_inverse(X2)),
inference(forward_demodulation,[],[f2012,f1982]) ).
fof(f2012,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(multiply(X0,multiply(X1,X2)),additive_inverse(multiply(multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f2011,f7]) ).
fof(f2011,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2)))),additive_inverse(multiply(multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f2010,f17]) ).
fof(f17,axiom,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2010,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2)))),multiply(additive_inverse(multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f1950,f17]) ).
fof(f1950,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2)))),multiply(multiply(additive_inverse(X0),X1),X2)),
inference(superposition,[],[f24,f17]) ).
fof(f5319,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = additive_inverse(associator(additive_inverse(X2),X1,X0)),
inference(superposition,[],[f5253,f4975]) ).
fof(f4975,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,X2,additive_inverse(X1)),
inference(forward_demodulation,[],[f4927,f7]) ).
fof(f4927,plain,
! [X2,X0,X1] : additive_inverse(additive_inverse(associator(X0,X1,X2))) = associator(X0,X2,additive_inverse(X1)),
inference(superposition,[],[f4832,f2041]) ).
fof(f2041,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = additive_inverse(associator(X2,X0,X1)),
inference(backward_demodulation,[],[f2000,f2039]) ).
fof(f2000,plain,
! [X2,X0,X1] : associator(X2,X0,additive_inverse(X1)) = associator(X2,additive_inverse(X0),X1),
inference(forward_demodulation,[],[f1999,f1982]) ).
fof(f1999,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = add(multiply(X2,multiply(X0,X1)),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1998,f7]) ).
fof(f1998,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = add(additive_inverse(additive_inverse(multiply(X2,multiply(X0,X1)))),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1997,f18]) ).
fof(f1997,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = add(additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1)))),additive_inverse(multiply(multiply(X2,X0),X1))),
inference(forward_demodulation,[],[f1996,f17]) ).
fof(f1996,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = add(additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1)))),multiply(additive_inverse(multiply(X2,X0)),X1)),
inference(forward_demodulation,[],[f1945,f18]) ).
fof(f1945,plain,
! [X2,X0,X1] : associator(X2,additive_inverse(X0),X1) = add(additive_inverse(multiply(X2,additive_inverse(multiply(X0,X1)))),multiply(multiply(X2,additive_inverse(X0)),X1)),
inference(superposition,[],[f24,f17]) ).
fof(f2077,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(associator(X0,X1,multiply(X1,X2))),associator(X0,multiply(X1,X1),X2)),
inference(forward_demodulation,[],[f2076,f328]) ).
fof(f2076,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(associator(X0,X1,multiply(X1,X2))),add(additive_inverse(multiply(X0,multiply(X1,multiply(X1,X2)))),add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,multiply(X1,X1),X2)))),
inference(forward_demodulation,[],[f2075,f11]) ).
fof(f2075,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(add(additive_inverse(associator(X0,X1,multiply(X1,X2))),additive_inverse(multiply(X0,multiply(X1,multiply(X1,X2))))),add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,multiply(X1,X1),X2))),
inference(forward_demodulation,[],[f2074,f163]) ).
fof(f2074,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,multiply(X1,X1),X2))),
inference(forward_demodulation,[],[f2073,f1]) ).
fof(f2073,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,multiply(X1,multiply(X1,X2))),add(additive_identity,associator(X0,multiply(X1,X1),X2)))),
inference(forward_demodulation,[],[f2072,f4]) ).
fof(f4,axiom,
! [X0] : additive_identity = multiply(X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2072,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,multiply(X1,multiply(X1,X2))),add(multiply(X0,additive_identity),associator(X0,multiply(X1,X1),X2)))),
inference(forward_demodulation,[],[f2071,f2015]) ).
fof(f2071,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,multiply(X1,multiply(X1,X2))),add(multiply(X0,associator(X1,X1,X2)),associator(X0,multiply(X1,X1),X2)))),
inference(forward_demodulation,[],[f2070,f11]) ).
fof(f2070,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(add(multiply(X0,multiply(X1,multiply(X1,X2))),multiply(X0,associator(X1,X1,X2))),associator(X0,multiply(X1,X1),X2))),
inference(forward_demodulation,[],[f2069,f8]) ).
fof(f2069,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,add(multiply(X1,multiply(X1,X2)),associator(X1,X1,X2))),associator(X0,multiply(X1,X1),X2))),
inference(forward_demodulation,[],[f2068,f1955]) ).
fof(f2068,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),add(multiply(X0,multiply(multiply(X1,X1),X2)),associator(X0,multiply(X1,X1),X2))),
inference(forward_demodulation,[],[f2027,f1955]) ).
fof(f2027,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))),multiply(multiply(X0,multiply(X1,X1)),X2)),
inference(backward_demodulation,[],[f1951,f1955]) ).
fof(f1951,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))),multiply(multiply(X0,multiply(X1,X1)),X2)),
inference(superposition,[],[f24,f12]) ).
fof(f8149,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(additive_inverse(associator(multiply(x,x),y,z)),add(additive_inverse(associator(x,z,multiply(x,y))),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f8148,f11]) ).
fof(f8148,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(add(additive_inverse(associator(multiply(x,x),y,z)),additive_inverse(associator(x,z,multiply(x,y)))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f8126,f163]) ).
fof(f8126,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(additive_inverse(add(associator(x,z,multiply(x,y)),associator(multiply(x,x),y,z))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f6680,f7954]) ).
fof(f7954,plain,
! [X2,X0,X1] : multiply(X0,associator(X0,X2,X1)) = add(associator(X0,X1,multiply(X0,X2)),associator(multiply(X0,X0),X2,X1)),
inference(superposition,[],[f70,f4853]) ).
fof(f4853,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(associator(X0,X2,multiply(X0,X1))),multiply(X0,associator(X0,X1,X2))),
inference(backward_demodulation,[],[f2111,f4850]) ).
fof(f4850,plain,
! [X2,X3,X0,X1] : add(X3,associator(X0,X1,X2)) = add(additive_inverse(associator(X0,X2,X1)),X3),
inference(forward_demodulation,[],[f4759,f2]) ).
fof(f4759,plain,
! [X2,X3,X0,X1] : add(X3,associator(X0,X1,X2)) = add(additive_inverse(associator(X0,X2,X1)),add(X3,additive_identity)),
inference(superposition,[],[f419,f4711]) ).
fof(f2111,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(X0,associator(X0,X1,X2)),associator(X0,multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f2110,f328]) ).
fof(f2110,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(multiply(X0,multiply(X0,multiply(X1,X2))),add(multiply(X0,associator(X0,X1,X2)),associator(X0,multiply(X0,X1),X2)))),
inference(forward_demodulation,[],[f2109,f11]) ).
fof(f2109,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(add(multiply(X0,multiply(X0,multiply(X1,X2))),multiply(X0,associator(X0,X1,X2))),associator(X0,multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f2108,f8]) ).
fof(f2108,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(multiply(X0,add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2))),associator(X0,multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f2033,f1955]) ).
fof(f2033,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(multiply(X0,multiply(multiply(X0,X1),X2)),associator(X0,multiply(X0,X1),X2))),
inference(backward_demodulation,[],[f2009,f1955]) ).
fof(f2009,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),multiply(multiply(X0,multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f1949,f13]) ).
fof(f1949,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),multiply(multiply(multiply(X0,X0),X1),X2)),
inference(superposition,[],[f24,f13]) ).
fof(f6680,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(additive_inverse(multiply(x,associator(x,y,z))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f6677,f18]) ).
fof(f6677,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(multiply(x,additive_inverse(associator(x,y,z))),associator(x,y,multiply(z,x)))),
inference(superposition,[],[f5483,f4832]) ).
fof(f5483,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(multiply(x,associator(x,z,y)),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f5387,f5425]) ).
fof(f5425,plain,
! [X2,X0,X1] : associator(X1,X2,X0) = additive_inverse(associator(X2,X1,X0)),
inference(superposition,[],[f5382,f5253]) ).
fof(f5387,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(z,x,multiply(x,y)),add(multiply(x,associator(x,z,y)),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f5264,f5382]) ).
fof(f5264,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(z,x,multiply(x,y)),add(multiply(x,associator(y,x,z)),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f5258,f7]) ).
fof(f5258,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(additive_inverse(associator(z,x,multiply(x,y)))),add(multiply(x,associator(y,x,z)),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f4984,f5253]) ).
fof(f4984,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(multiply(x,y),x,z)),add(multiply(x,associator(y,x,z)),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f4983,f7]) ).
fof(f4983,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(additive_inverse(multiply(x,associator(y,x,z)))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f4982,f18]) ).
fof(f4982,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(multiply(x,additive_inverse(associator(y,x,z)))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f4977,f2039]) ).
fof(f4977,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(multiply(x,associator(y,x,additive_inverse(z)))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f4973,f4975]) ).
fof(f4973,plain,
add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))) != additive_inverse(associator(x,z,multiply(x,y))),
inference(forward_demodulation,[],[f4968,f2041]) ).
fof(f4968,plain,
add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))) != associator(x,additive_inverse(z),multiply(x,y)),
inference(backward_demodulation,[],[f4836,f4965]) ).
fof(f4965,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X0,additive_inverse(X2),X1),
inference(forward_demodulation,[],[f4926,f7]) ).
fof(f4926,plain,
! [X2,X0,X1] : additive_inverse(additive_inverse(associator(X0,X1,X2))) = associator(X0,additive_inverse(X2),X1),
inference(superposition,[],[f4832,f2039]) ).
fof(f4836,plain,
associator(x,multiply(x,y),z) != add(additive_inverse(associator(multiply(x,y),x,z)),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f4791,f4832]) ).
fof(f4791,plain,
associator(x,multiply(x,y),z) != add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f4790,f1]) ).
fof(f4790,plain,
associator(x,multiply(x,y),z) != add(additive_identity,add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f4781,f35]) ).
fof(f35,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f6,f1]) ).
fof(f4781,plain,
associator(x,multiply(x,y),z) != add(additive_inverse(additive_identity),add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x))))),
inference(backward_demodulation,[],[f2174,f4779]) ).
fof(f2174,plain,
associator(x,multiply(x,y),z) != add(additive_inverse(associator(x,multiply(y,z),x)),add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x))))),
inference(superposition,[],[f2129,f66]) ).
fof(f2129,plain,
associator(x,multiply(x,y),z) != add(additive_inverse(associator(x,multiply(y,z),x)),add(additive_inverse(multiply(x,associator(y,z,x))),add(associator(x,y,multiply(z,x)),associator(multiply(x,y),z,x)))),
inference(backward_demodulation,[],[f23,f2128]) ).
fof(f2128,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(additive_inverse(multiply(X0,associator(X1,X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))),
inference(forward_demodulation,[],[f2127,f328]) ).
fof(f2127,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(additive_inverse(multiply(X0,associator(X1,X2,X3))),add(additive_inverse(multiply(X0,multiply(X1,multiply(X2,X3)))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))))),
inference(forward_demodulation,[],[f2126,f11]) ).
fof(f2126,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(add(additive_inverse(multiply(X0,associator(X1,X2,X3))),additive_inverse(multiply(X0,multiply(X1,multiply(X2,X3))))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3))))),
inference(forward_demodulation,[],[f2125,f163]) ).
fof(f2125,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(additive_inverse(add(multiply(X0,multiply(X1,multiply(X2,X3))),multiply(X0,associator(X1,X2,X3)))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3))))),
inference(forward_demodulation,[],[f2124,f8]) ).
fof(f2124,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(additive_inverse(multiply(X0,add(multiply(X1,multiply(X2,X3)),associator(X1,X2,X3)))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3))))),
inference(forward_demodulation,[],[f2123,f1955]) ).
fof(f2123,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(associator(X0,multiply(X1,X2),X3)),add(additive_inverse(multiply(X0,multiply(multiply(X1,X2),X3))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3))))),
inference(forward_demodulation,[],[f2122,f11]) ).
fof(f2122,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(add(additive_inverse(associator(X0,multiply(X1,X2),X3)),additive_inverse(multiply(X0,multiply(multiply(X1,X2),X3)))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))),
inference(forward_demodulation,[],[f2121,f163]) ).
fof(f2121,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(add(multiply(X0,multiply(multiply(X1,X2),X3)),associator(X0,multiply(X1,X2),X3))),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))),
inference(forward_demodulation,[],[f2120,f1955]) ).
fof(f2120,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(additive_inverse(multiply(multiply(X0,multiply(X1,X2)),X3)),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))),
inference(forward_demodulation,[],[f2119,f17]) ).
fof(f2119,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3),add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),associator(multiply(X0,X1),X2,X3)))),
inference(forward_demodulation,[],[f2118,f11]) ).
fof(f2118,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3),add(add(multiply(X0,multiply(X1,multiply(X2,X3))),associator(X0,X1,multiply(X2,X3))),associator(multiply(X0,X1),X2,X3))),
inference(forward_demodulation,[],[f2117,f1955]) ).
fof(f2117,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3),add(multiply(multiply(X0,X1),multiply(X2,X3)),associator(multiply(X0,X1),X2,X3))),
inference(forward_demodulation,[],[f1957,f1955]) ).
fof(f1957,plain,
! [X2,X3,X0,X1] : add(multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3),multiply(multiply(multiply(X0,X1),X2),X3)) = multiply(associator(X0,X1,X2),X3),
inference(superposition,[],[f9,f24]) ).
fof(f23,axiom,
associator(x,multiply(x,y),z) != multiply(associator(x,y,z),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG027-9 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.13 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Jun 18 14:40:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.12/0.36 Running first-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1874)dis+10_577:524288_drc=encompass:sil=256000:sp=const_frequency:spb=units:i=214:doe=on:bd=off:av=off:dpc=on:irc=eager:uhcvi=on:ss=included:rawr=on:to=lpo:slsq=on:slsqr=8,31:s2agt=5:s2at=4.0:fdi=2_0 on theBenchmark for (3000ds/214Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1871)lrs+10_3:107_sil=64000:i=143:ss=axioms:sgt=16:rawr=on:to=lpo:drc=encompass_0 on theBenchmark for (3000ds/143Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1868)dis+10_28091:1048576_to=lpo:drc=encompass:sil=128000:tgt=full:erd=off:cond=on:i=107869:doe=on:ins=2:av=off:dpc=on:irc=eager:s2pl=on:s2agt=5:s2at=4.0:foolp=on_0 on theBenchmark for (3000ds/107869Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1872)lrs+10_2:1_to=lpo:drc=encompass:sil=4000:tgt=full:sp=const_min:urr=on:nwc=5.0:i=129:rawr=on_0 on theBenchmark for (3000ds/129Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1873)lrs+10_1:12_drc=encompass:sil=256000:tgt=full:spb=intro:i=735:kws=precedence:awrs=converge:awrsf=500:irc=lazy_0 on theBenchmark for (3000ds/735Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1869)lrs+10_1:1_drc=encompass:sil=256000:tgt=ground:sp=unary_first:sos=on:i=220312:kws=precedence:lwlo=on:irc=lazy_0 on theBenchmark for (3000ds/220312Mi)
% 0.21/0.43 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (1870)lrs+10_16:1_sfv=off:sil=2000:sp=reverse_frequency:urr=ec_only:br=off:i=126:doe=on:irc=lazy:to=lpo:fd=preordered:bd=preordered:fsd=on:drc=encompass_0 on theBenchmark for (3000ds/126Mi)
% 0.21/0.43 % (1869)Refutation not found, incomplete strategy% (1869)------------------------------
% 0.21/0.43 % (1869)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.43 % (1869)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.43 % (1869)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43 % (1869)Memory used [KB]: 833
% 0.21/0.43 % (1869)Time elapsed: 0.005 s
% 0.21/0.43 % (1869)Instructions burned: 4 (million)
% 0.21/0.43 % (1869)------------------------------
% 0.21/0.43 % (1869)------------------------------
% 0.21/0.49 % (1870)Instruction limit reached!
% 0.21/0.49 % (1870)------------------------------
% 0.21/0.49 % (1870)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.49 % (1870)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.49 % (1870)Termination reason: Time limit
% 0.21/0.49 % (1870)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (1870)Memory used [KB]: 2600
% 0.21/0.49 % (1870)Time elapsed: 0.066 s
% 0.21/0.49 % (1870)Instructions burned: 128 (million)
% 0.21/0.49 % (1872)Instruction limit reached!
% 0.21/0.49 % (1872)------------------------------
% 0.21/0.49 % (1872)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.49 % (1872)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.49 % (1872)Termination reason: Time limit
% 0.21/0.49 % (1872)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (1872)Memory used [KB]: 1940
% 0.21/0.49 % (1872)Time elapsed: 0.070 s
% 0.21/0.49 % (1872)Instructions burned: 129 (million)
% 0.21/0.50 % (1871)Instruction limit reached!
% 0.21/0.50 % (1871)------------------------------
% 0.21/0.50 % (1871)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.50 % (1871)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.50 % (1871)Termination reason: Time limit
% 0.21/0.50 % (1871)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (1871)Memory used [KB]: 1192
% 0.21/0.50 % (1871)Time elapsed: 0.071 s
% 0.21/0.50 % (1871)Instructions burned: 145 (million)
% 0.21/0.50 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.50 % (1875)lrs+10_1:64_sil=8000:tgt=full:spb=non_intro:i=204:kws=precedence:plsq=on:awrs=converge:awrsf=30:sp=weighted_frequency:drc=encompass:irc=eager_0 on theBenchmark for (2999ds/204Mi)
% 0.21/0.51 % (1874)Instruction limit reached!
% 0.21/0.51 % (1874)------------------------------
% 0.21/0.51 % (1874)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.51 % (1874)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.51 % (1874)Termination reason: Time limit
% 0.21/0.51 % (1874)Termination phase: Saturation
% 0.21/0.51
% 0.21/0.51 % (1874)Memory used [KB]: 2645
% 0.21/0.51 % (1874)Time elapsed: 0.083 s
% 0.21/0.51 % (1874)Instructions burned: 215 (million)
% 0.21/0.53 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.53 % (1876)lrs+10_1:1_to=lpo:drc=encompass:sil=2000:fde=unused:sp=const_min:i=444:fd=preordered:irc=eager:bd=preordered:ss=axioms_0 on theBenchmark for (2998ds/444Mi)
% 0.21/0.53 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.53 % (1877)lrs+10_3:58_drc=encompass:sil=256000:tgt=full:bsd=on:sp=reverse_arity:lwlo=on:s2a=on:i=365:s2at=2.0:kws=precedence:bsr=on:irw=on:dpc=on:fibus=on:doe=on:bs=on:br=off:erd=off:s2agt=20:nwc=8.95214440448525:cond=fast:foolp=on:spb=non_intro:sfv=off:irc=lazy:fde=unused:ins=3_0 on theBenchmark for (2998ds/365Mi)
% 0.21/0.53 % (1867)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.53 % (1878)lrs+10_3:4_to=lpo:drc=encompass:sil=4000:sp=reverse_frequency:i=390:ss=axioms:sgt=16:s2a=on:s2at=3.0:irc=lazy:bd=off_0 on theBenchmark for (2998ds/390Mi)
% 1.31/0.54 % (1867)Running in auto input_syntax mode. Trying TPTP
% 1.31/0.54 % (1879)lrs+10_1:4_to=lpo:drc=encompass:sil=4000:tgt=full:i=2789:bd=preordered:fd=preordered_0 on theBenchmark for (2998ds/2789Mi)
% 1.47/0.57 % (1875)Instruction limit reached!
% 1.47/0.57 % (1875)------------------------------
% 1.47/0.57 % (1875)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.47/0.57 % (1875)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.47/0.57 % (1875)Termination reason: Time limit
% 1.47/0.57 % (1875)Termination phase: Saturation
% 1.47/0.57
% 1.47/0.57 % (1875)Memory used [KB]: 2763
% 1.47/0.57 % (1875)Time elapsed: 0.092 s
% 1.47/0.57 % (1875)Instructions burned: 204 (million)
% 1.47/0.60 % (1867)Running in auto input_syntax mode. Trying TPTP
% 1.47/0.60 % (1880)lrs+10_1:3_drc=encompass:sil=256000:tgt=ground:sp=unary_first:i=975:ss=axioms:sgt=10:rawr=on:urr=on:ins=1:plsq=on:dpc=on:spb=intro:sd=4:fsr=off:bs=on:kws=inv_arity:irc=lazy:nwc=5.0_0 on theBenchmark for (2997ds/975Mi)
% 1.90/0.64 % (1878)Instruction limit reached!
% 1.90/0.64 % (1878)------------------------------
% 1.90/0.64 % (1878)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.90/0.64 % (1878)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.90/0.64 % (1878)Termination reason: Time limit
% 1.90/0.64 % (1878)Termination phase: Saturation
% 1.90/0.64
% 1.90/0.64 % (1878)Memory used [KB]: 3097
% 1.90/0.64 % (1878)Time elapsed: 0.112 s
% 1.90/0.64 % (1878)Instructions burned: 391 (million)
% 1.90/0.65 % (1877)Instruction limit reached!
% 1.90/0.65 % (1877)------------------------------
% 1.90/0.65 % (1877)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.90/0.65 % (1877)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.90/0.65 % (1877)Termination reason: Time limit
% 1.90/0.65 % (1877)Termination phase: Saturation
% 1.90/0.65
% 1.90/0.65 % (1877)Memory used [KB]: 3662
% 1.90/0.65 % (1877)Time elapsed: 0.150 s
% 1.90/0.65 % (1877)Instructions burned: 366 (million)
% 2.09/0.68 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.09/0.68 % (1881)lrs+10_1:24_drc=encompass:sil=256000:tgt=full:sp=unary_frequency:spb=non_intro:i=6970:ins=2:fsr=off:kws=precedence:irc=eager:bsr=unit_only:br=off:ss=included:sgt=16:bd=preordered_0 on theBenchmark for (2997ds/6970Mi)
% 2.09/0.69 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.09/0.69 % (1882)lrs+10_7:24_to=lpo:drc=encompass:sil=128000:fde=unused:sp=const_min:spb=goal:i=522:irc=lazy:slsq=on:fdi=256:nwc=10.0:dpc=on:ss=included:st=2.0_0 on theBenchmark for (2997ds/522Mi)
% 2.09/0.70 % (1876)Instruction limit reached!
% 2.09/0.70 % (1876)------------------------------
% 2.09/0.70 % (1876)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.09/0.70 % (1876)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.09/0.70 % (1876)Termination reason: Time limit
% 2.09/0.70 % (1876)Termination phase: Saturation
% 2.09/0.70
% 2.09/0.70 % (1876)Memory used [KB]: 5688
% 2.09/0.70 % (1876)Time elapsed: 0.187 s
% 2.09/0.70 % (1876)Instructions burned: 445 (million)
% 2.09/0.71 % (1873)Instruction limit reached!
% 2.09/0.71 % (1873)------------------------------
% 2.09/0.71 % (1873)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.09/0.71 % (1873)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.09/0.71 % (1873)Termination reason: Time limit
% 2.09/0.71 % (1873)Termination phase: Saturation
% 2.09/0.71
% 2.09/0.71 % (1873)Memory used [KB]: 7955
% 2.09/0.71 % (1873)Time elapsed: 0.289 s
% 2.09/0.71 % (1873)Instructions burned: 735 (million)
% 2.09/0.73 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.09/0.73 % (1883)lrs+10_1:1024_drc=encompass:sil=8000:tgt=ground:fde=unused:sp=const_min:spb=goal:kmz=on:i=1381:kws=inv_arity:awrs=converge:awrsf=200:irc=eager_0 on theBenchmark for (2996ds/1381Mi)
% 2.32/0.75 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.32/0.75 % (1884)lrs+10_1:4_to=lpo:drc=encompass:sil=128000:fde=unused:sp=const_min:spb=goal:fd=preordered:i=589:irc=lazy:slsq=on:slsqr=1,4_0 on theBenchmark for (2996ds/589Mi)
% 2.51/0.84 % (1882)Instruction limit reached!
% 2.51/0.84 % (1882)------------------------------
% 2.51/0.84 % (1882)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.51/0.84 % (1882)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.51/0.84 % (1882)Termination reason: Time limit
% 2.51/0.84 % (1882)Termination phase: Saturation
% 2.51/0.84
% 2.51/0.84 % (1882)Memory used [KB]: 3235
% 2.51/0.84 % (1882)Time elapsed: 0.148 s
% 2.51/0.84 % (1882)Instructions burned: 523 (million)
% 2.78/0.87 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.78/0.87 % (1885)lrs+10_1:4_bsr=on:slsqr=2,7:to=lpo:drc=encompass:sil=16000:tgt=full:sp=unary_first:spb=goal:slsq=on:i=659:slsql=off:ins=2:irc=eager:rawr=on:nwc=8.7296035496261:erd=off:s2pl=no:cond=fast:plsq=on:sims=off_0 on theBenchmark for (2995ds/659Mi)
% 2.78/0.88 % (1884)First to succeed.
% 2.78/0.88 % (1884)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1867"
% 2.78/0.89 % (1867)Running in auto input_syntax mode. Trying TPTP
% 2.78/0.89 % (1884)Refutation found. Thanks to Tanya!
% 2.78/0.89 % SZS status Unsatisfiable for theBenchmark
% 2.78/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/0.89 % (1884)------------------------------
% 2.78/0.89 % (1884)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.78/0.89 % (1884)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.78/0.89 % (1884)Termination reason: Refutation
% 2.78/0.89
% 2.78/0.89 % (1884)Memory used [KB]: 3459
% 2.78/0.89 % (1884)Time elapsed: 0.136 s
% 2.78/0.89 % (1884)Instructions burned: 448 (million)
% 2.78/0.89 % (1884)------------------------------
% 2.78/0.89 % (1884)------------------------------
% 2.78/0.89 % (1867)Success in time 0.525 s
%------------------------------------------------------------------------------