%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG027-8 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Tue Sep 29 12:35:11 PM UTC 2026
% Result : Unsatisfiable 52.66s 8.38s
% Output : Refutation 53.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 181 ( 181 unt; 0 def)
% Number of atoms : 181 ( 180 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 : 10 ( 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 : 461 ( 461 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f3,axiom,
! [X0] : multiply(additive_identity,X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f4,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f16,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
fof(f17,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
fof(f18,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',associator) ).
fof(f20,negated_conjecture,
associator(x,multiply(x,y),z) != multiply(associator(x,y,z),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_moufang) ).
fof(f23,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(multiply(X0,multiply(add(X1,X2),X3)))),
inference(superposition,[],[f18,f12]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(add(multiply(multiply(X0,X1),X2),multiply(multiply(X0,X1),X3)),additive_inverse(multiply(X0,multiply(X1,add(X2,X3))))),
inference(superposition,[],[f18,f12]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),additive_inverse(multiply(X0,multiply(X1,add(X2,X3)))))),
inference(forward_demodulation,[],[f24,f15]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(multiply(X0,add(multiply(X1,X3),multiply(X2,X3))))),
inference(forward_demodulation,[],[f23,f13]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),additive_inverse(multiply(X0,add(multiply(X1,X2),multiply(X1,X3)))))),
inference(forward_demodulation,[],[f25,f12]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(add(multiply(X0,X1),multiply(X0,X2)),X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))),
inference(forward_demodulation,[],[f26,f12]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(multiply(X0,X1),X2),add(multiply(multiply(X0,X1),X3),additive_inverse(add(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3)))))),
inference(forward_demodulation,[],[f28,f12]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(add(multiply(multiply(X0,X1),X3),multiply(multiply(X0,X2),X3)),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))),
inference(forward_demodulation,[],[f29,f13]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(multiply(X0,X1),X3),add(multiply(multiply(X0,X2),X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3)))))),
inference(forward_demodulation,[],[f32,f15]) ).
fof(f39,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(additive_inverse(multiply(X0,multiply(X1,X2))),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f18,f14]) ).
fof(f46,plain,
! [X0,X1] : associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),additive_inverse(multiply(X0,multiply(X1,X1)))),
inference(superposition,[],[f18,f16]) ).
fof(f48,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(multiply(X0,multiply(X1,X1)),X2),additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2)))),
inference(superposition,[],[f18,f16]) ).
fof(f52,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X1),
inference(forward_demodulation,[],[f46,f10]) ).
fof(f94,plain,
! [X0,X1] : associator(X0,X0,X1) = add(multiply(X0,multiply(X0,X1)),additive_inverse(multiply(X0,multiply(X0,X1)))),
inference(superposition,[],[f18,f17]) ).
fof(f99,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(multiply(multiply(X0,X0),X1),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2))))),
inference(superposition,[],[f18,f17]) ).
fof(f100,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(multiply(X0,multiply(X0,X1)),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2))))),
inference(forward_demodulation,[],[f99,f17]) ).
fof(f104,plain,
! [X0,X1] : additive_identity = associator(X0,X0,X1),
inference(forward_demodulation,[],[f94,f10]) ).
fof(f131,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(multiply(X0,X1),X2),X3),multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3)) = multiply(associator(X0,X1,X2),X3),
inference(superposition,[],[f13,f18]) ).
fof(f184,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f187,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),add(additive_inverse(multiply(X0,multiply(X1,X2))),X3)) = add(associator(X0,X1,X2),X3),
inference(superposition,[],[f15,f18]) ).
fof(f192,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f200,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[],[f184,f15]) ).
fof(f205,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),X3) = add(additive_inverse(multiply(X0,multiply(X1,X2))),add(multiply(multiply(X0,X1),X2),X3)),
inference(backward_demodulation,[],[f187,f200]) ).
fof(f262,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[],[f15,f10]) ).
fof(f265,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f1,f10]) ).
fof(f266,plain,
! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
inference(superposition,[],[f15,f10]) ).
fof(f271,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f262,f1]) ).
fof(f276,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f277,plain,
! [X0,X1] : multiply(additive_identity,X1) = add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),
inference(superposition,[],[f13,f8]) ).
fof(f282,plain,
! [X0,X1] : additive_identity = add(multiply(additive_inverse(X0),X1),multiply(X0,X1)),
inference(forward_demodulation,[],[f277,f4]) ).
fof(f283,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f276,f1]) ).
fof(f286,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f283,f14]) ).
fof(f291,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),X3) = add(additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2)))),add(associator(X0,X1,X2),X3)),
inference(superposition,[],[f283,f205]) ).
fof(f299,plain,
! [X0,X1] : add(add(X1,X0),additive_inverse(X1)) = X0,
inference(superposition,[],[f14,f283]) ).
fof(f302,plain,
! [X0,X1] : add(X1,add(X0,additive_inverse(X1))) = X0,
inference(forward_demodulation,[],[f299,f15]) ).
fof(f309,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),X3) = add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),X3)),
inference(forward_demodulation,[],[f291,f11]) ).
fof(f321,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),add(multiply(multiply(X0,X1),X3),additive_inverse(add(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3))))))),
inference(backward_demodulation,[],[f31,f309]) ).
fof(f322,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(multiply(multiply(X0,X2),X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3))))))),
inference(backward_demodulation,[],[f34,f309]) ).
fof(f327,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(multiply(X0,X1),multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3))),
inference(backward_demodulation,[],[f131,f309]) ).
fof(f331,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(X0,multiply(multiply(X1,X1),X2)),add(associator(X0,multiply(X1,X1),X2),additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))))),
inference(backward_demodulation,[],[f48,f309]) ).
fof(f334,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(X0,multiply(multiply(X0,X1),X2)),add(associator(X0,multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))))),
inference(backward_demodulation,[],[f100,f309]) ).
fof(f337,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(X0,multiply(X1,multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))))),
inference(forward_demodulation,[],[f331,f17]) ).
fof(f340,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),multiply(additive_inverse(multiply(X0,multiply(X1,X2))),X3)))),
inference(forward_demodulation,[],[f327,f309]) ).
fof(f342,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(multiply(X0,multiply(X2,X3)),add(associator(X0,X2,X3),additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X0,multiply(X2,X3)))))))),
inference(forward_demodulation,[],[f322,f309]) ).
fof(f343,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),additive_inverse(add(multiply(X0,multiply(X1,X2)),multiply(X0,multiply(X1,X3)))))))),
inference(forward_demodulation,[],[f321,f309]) ).
fof(f363,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X0,X1)),X0),
inference(superposition,[],[f286,f286]) ).
fof(f415,plain,
! [X2,X0,X1] : add(X0,X1) = add(X2,add(X0,add(X1,additive_inverse(X2)))),
inference(superposition,[],[f302,f15]) ).
fof(f468,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(superposition,[],[f286,f282]) ).
fof(f469,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(forward_demodulation,[],[f468,f2]) ).
fof(f484,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),additive_inverse(multiply(multiply(X0,multiply(X1,X2)),X3))))),
inference(backward_demodulation,[],[f340,f469]) ).
fof(f508,plain,
! [X2,X0,X1] : add(multiply(additive_inverse(X0),X1),multiply(additive_inverse(X0),X2)) = additive_inverse(multiply(X0,add(X1,X2))),
inference(superposition,[],[f12,f469]) ).
fof(f509,plain,
! [X2,X0,X1] : add(multiply(additive_inverse(X0),X1),multiply(additive_inverse(X0),X2)) = additive_inverse(add(multiply(X0,X1),multiply(X0,X2))),
inference(forward_demodulation,[],[f508,f12]) ).
fof(f514,plain,
! [X2,X0,X1] : additive_inverse(add(multiply(X0,X1),multiply(X0,X2))) = add(multiply(additive_inverse(X0),X1),additive_inverse(multiply(X0,X2))),
inference(forward_demodulation,[],[f509,f469]) ).
fof(f518,plain,
! [X2,X0,X1] : additive_inverse(add(multiply(X0,X1),multiply(X0,X2))) = add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))),
inference(forward_demodulation,[],[f514,f469]) ).
fof(f522,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(multiply(X0,multiply(X2,X3)),add(associator(X0,X2,X3),add(additive_inverse(multiply(X0,multiply(X1,X3))),additive_inverse(multiply(X0,multiply(X2,X3)))))))),
inference(backward_demodulation,[],[f342,f518]) ).
fof(f524,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(additive_inverse(multiply(X0,multiply(X1,X2))),additive_inverse(multiply(X0,multiply(X1,X3)))))))),
inference(backward_demodulation,[],[f343,f518]) ).
fof(f525,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(multiply(X0,multiply(X1,X2)),add(associator(X0,X1,X2),add(associator(X0,X1,X3),additive_inverse(multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f524,f415]) ).
fof(f527,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(associator(X0,X2,X3),additive_inverse(multiply(X0,multiply(X1,X3)))))),
inference(forward_demodulation,[],[f522,f415]) ).
fof(f529,plain,
! [X2,X3,X0,X1] : associator(X0,X1,add(X2,X3)) = add(associator(X0,X1,X2),associator(X0,X1,X3)),
inference(forward_demodulation,[],[f525,f415]) ).
fof(f531,plain,
! [X2,X3,X0,X1] : associator(X0,add(X1,X2),X3) = add(associator(X0,X1,X3),associator(X0,X2,X3)),
inference(forward_demodulation,[],[f527,f415]) ).
fof(f550,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,add(X1,X2)),associator(X0,X2,add(X1,X2))),
inference(superposition,[],[f52,f531]) ).
fof(f551,plain,
! [X2,X0,X1] : additive_identity = add(associator(add(X0,X1),X0,X2),associator(add(X0,X1),X1,X2)),
inference(superposition,[],[f104,f531]) ).
fof(f552,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,add(X1,X2)),add(associator(X0,X2,X1),associator(X0,X2,X2))),
inference(forward_demodulation,[],[f550,f529]) ).
fof(f561,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,add(X1,X2)),add(associator(X0,X2,X1),additive_identity)),
inference(forward_demodulation,[],[f552,f52]) ).
fof(f564,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,add(X1,X2)),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f561,f2]) ).
fof(f567,plain,
! [X2,X0,X1] : additive_identity = add(add(associator(X0,X1,X1),associator(X0,X1,X2)),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f564,f529]) ).
fof(f569,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,X1),add(associator(X0,X1,X2),associator(X0,X2,X1))),
inference(forward_demodulation,[],[f567,f15]) ).
fof(f571,plain,
! [X2,X0,X1] : additive_identity = add(additive_identity,add(associator(X0,X1,X2),associator(X0,X2,X1))),
inference(forward_demodulation,[],[f569,f52]) ).
fof(f573,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X1,X2),associator(X0,X2,X1)),
inference(forward_demodulation,[],[f571,f1]) ).
fof(f635,plain,
! [X2,X0,X1] : add(associator(X0,X1,X2),associator(X0,X1,additive_inverse(X2))) = associator(X0,X1,additive_identity),
inference(superposition,[],[f529,f10]) ).
fof(f697,plain,
! [X2,X0,X1] : associator(X0,X1,additive_inverse(X2)) = add(additive_inverse(associator(X0,X1,X2)),associator(X0,X1,additive_identity)),
inference(superposition,[],[f283,f635]) ).
fof(f831,plain,
! [X0,X1] : additive_identity = add(associator(X0,X1,X0),additive_identity),
inference(superposition,[],[f573,f104]) ).
fof(f842,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),add(associator(X0,X2,X1),X3)) = add(additive_identity,X3),
inference(superposition,[],[f15,f573]) ).
fof(f844,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = add(additive_inverse(associator(X0,X1,X2)),additive_identity),
inference(superposition,[],[f286,f573]) ).
fof(f847,plain,
! [X2,X0,X1] : associator(X0,X2,X1) = additive_inverse(associator(X0,X1,X2)),
inference(forward_demodulation,[],[f844,f2]) ).
fof(f849,plain,
! [X2,X3,X0,X1] : add(associator(X0,X1,X2),add(associator(X0,X2,X1),X3)) = X3,
inference(forward_demodulation,[],[f842,f1]) ).
fof(f854,plain,
! [X0,X1] : additive_identity = associator(X0,X1,X0),
inference(forward_demodulation,[],[f831,f2]) ).
fof(f860,plain,
multiply(associator(x,y,z),x) != additive_inverse(associator(x,z,multiply(x,y))),
inference(backward_demodulation,[],[f20,f847]) ).
fof(f966,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(multiply(add(X0,X2),multiply(X1,X3))),multiply(add(multiply(X0,X1),multiply(X2,X1)),X3)),
inference(superposition,[],[f39,f13]) ).
fof(f969,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(multiply(additive_inverse(X0),multiply(X1,X2))),multiply(additive_inverse(multiply(X0,X1)),X2)),
inference(superposition,[],[f39,f469]) ).
fof(f973,plain,
! [X0,X1] : associator(X0,X1,additive_identity) = add(additive_inverse(multiply(X0,multiply(X1,additive_identity))),additive_identity),
inference(superposition,[],[f39,f6]) ).
fof(f974,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)),
inference(superposition,[],[f271,f39]) ).
fof(f1004,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(X0,add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2))),add(associator(X0,multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))))),
inference(backward_demodulation,[],[f334,f974]) ).
fof(f1006,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),additive_inverse(add(multiply(X0,multiply(multiply(X1,X2),X3)),associator(X0,multiply(X1,X2),X3)))))),
inference(backward_demodulation,[],[f484,f974]) ).
fof(f1009,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(multiply(X0,multiply(X1,multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))))),
inference(backward_demodulation,[],[f337,f974]) ).
fof(f1010,plain,
! [X0,X1] : associator(X0,X1,additive_identity) = additive_inverse(multiply(X0,multiply(X1,additive_identity))),
inference(forward_demodulation,[],[f973,f2]) ).
fof(f1014,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(multiply(additive_inverse(X0),multiply(X1,X2))),additive_inverse(multiply(multiply(X0,X1),X2))),
inference(forward_demodulation,[],[f969,f469]) ).
fof(f1017,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(multiply(add(X0,X2),multiply(X1,X3))),add(multiply(multiply(X0,X1),X3),multiply(multiply(X2,X1),X3))),
inference(forward_demodulation,[],[f966,f13]) ).
fof(f1034,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),additive_inverse(add(multiply(X0,add(multiply(X1,multiply(X2,X3)),associator(X1,X2,X3))),associator(X0,multiply(X1,X2),X3)))))),
inference(forward_demodulation,[],[f1006,f974]) ).
fof(f1036,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(add(multiply(X0,multiply(X0,multiply(X1,X2))),multiply(X0,associator(X0,X1,X2))),add(associator(X0,multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1004,f12]) ).
fof(f1048,plain,
! [X0,X1] : associator(X0,X1,additive_identity) = additive_inverse(multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f1010,f6]) ).
fof(f1050,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(multiply(additive_inverse(X0),multiply(X1,X2))),additive_inverse(add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)))),
inference(forward_demodulation,[],[f1014,f974]) ).
fof(f1053,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(multiply(add(X0,X2),multiply(X1,X3))),add(multiply(multiply(X0,X1),X3),add(multiply(X2,multiply(X1,X3)),associator(X2,X1,X3)))),
inference(forward_demodulation,[],[f1017,f974]) ).
fof(f1070,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),additive_inverse(add(add(multiply(X0,multiply(X1,multiply(X2,X3))),multiply(X0,associator(X1,X2,X3))),associator(X0,multiply(X1,X2),X3)))))),
inference(forward_demodulation,[],[f1034,f12]) ).
fof(f1071,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(multiply(X0,multiply(X0,multiply(X1,X2))),add(multiply(X0,associator(X0,X1,X2)),add(associator(X0,multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2))))))),
inference(forward_demodulation,[],[f1036,f15]) ).
fof(f1079,plain,
! [X0,X1] : additive_inverse(additive_identity) = associator(X0,X1,additive_identity),
inference(forward_demodulation,[],[f1048,f6]) ).
fof(f1081,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(additive_inverse(additive_inverse(multiply(X0,multiply(X1,X2)))),additive_inverse(add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)))),
inference(forward_demodulation,[],[f1050,f469]) ).
fof(f1084,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(multiply(add(X0,X2),multiply(X1,X3))),add(add(multiply(X0,multiply(X1,X3)),associator(X0,X1,X3)),add(multiply(X2,multiply(X1,X3)),associator(X2,X1,X3)))),
inference(forward_demodulation,[],[f1053,f974]) ).
fof(f1099,plain,
! [X2,X3,X0,X1] : multiply(associator(X0,X1,X2),X3) = add(multiply(X0,multiply(X1,multiply(X2,X3))),add(associator(X0,X1,multiply(X2,X3)),add(associator(multiply(X0,X1),X2,X3),additive_inverse(add(multiply(X0,multiply(X1,multiply(X2,X3))),add(multiply(X0,associator(X1,X2,X3)),associator(X0,multiply(X1,X2),X3))))))),
inference(forward_demodulation,[],[f1070,f15]) ).
fof(f1100,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,[],[f1071,f415]) ).
fof(f1106,plain,
! [X0,X1] : additive_identity = associator(X0,X1,additive_identity),
inference(forward_demodulation,[],[f1079,f265]) ).
fof(f1108,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(multiply(X0,multiply(X1,X2)),additive_inverse(add(multiply(X0,multiply(X1,X2)),associator(X0,X1,X2)))),
inference(forward_demodulation,[],[f1081,f11]) ).
fof(f1111,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(multiply(add(X0,X2),multiply(X1,X3))),add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(multiply(X2,multiply(X1,X3)),associator(X2,X1,X3))))),
inference(forward_demodulation,[],[f1084,f15]) ).
fof(f1128,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(multiply(x,multiply(y,multiply(z,x))),add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),additive_inverse(add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,associator(y,z,x)),associator(x,multiply(y,z),x))))))),
inference(backward_demodulation,[],[f860,f1099]) ).
fof(f1135,plain,
! [X2,X0,X1] : associator(X0,X1,additive_inverse(X2)) = add(additive_inverse(associator(X0,X1,X2)),additive_identity),
inference(backward_demodulation,[],[f697,f1106]) ).
fof(f1144,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X2,multiply(X1,X3)))),add(multiply(X0,multiply(X1,X3)),add(associator(X0,X1,X3),add(multiply(X2,multiply(X1,X3)),associator(X2,X1,X3))))),
inference(forward_demodulation,[],[f1111,f13]) ).
fof(f1158,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(multiply(x,multiply(y,multiply(z,x))),add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),additive_inverse(add(multiply(x,multiply(y,multiply(z,x))),add(multiply(x,associator(y,z,x)),additive_identity)))))),
inference(forward_demodulation,[],[f1128,f854]) ).
fof(f1171,plain,
! [X2,X0,X1] : additive_inverse(associator(X0,X1,X2)) = associator(X0,X1,additive_inverse(X2)),
inference(forward_demodulation,[],[f1135,f2]) ).
fof(f1181,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(multiply(x,multiply(y,multiply(z,x))),add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),additive_inverse(add(multiply(x,multiply(y,multiply(z,x))),multiply(x,associator(y,z,x))))))),
inference(forward_demodulation,[],[f1158,f2]) ).
fof(f1198,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(multiply(x,multiply(y,multiply(z,x))),add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,multiply(y,multiply(z,x)))),additive_inverse(multiply(x,associator(y,z,x))))))),
inference(forward_demodulation,[],[f1181,f518]) ).
fof(f1274,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(multiply(x,multiply(y,multiply(z,x))),add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),additive_inverse(multiply(x,multiply(y,multiply(z,x)))))))),
inference(superposition,[],[f1198,f14]) ).
fof(f1316,plain,
! [X2,X0,X1] : multiply(X0,associator(X0,X1,X2)) = add(additive_inverse(associator(X0,multiply(X0,X1),X2)),associator(multiply(X0,X0),X1,X2)),
inference(superposition,[],[f286,f1100]) ).
fof(f1609,plain,
! [X2,X3,X0,X1] : add(add(X0,X1),add(X3,X2)) = add(X3,add(X0,add(X1,X2))),
inference(superposition,[],[f192,f192]) ).
fof(f1680,plain,
! [X2,X3,X0,X1] : add(X0,add(X1,add(X2,X3))) = add(X2,add(X3,add(X0,X1))),
inference(superposition,[],[f15,f192]) ).
fof(f1687,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(add(multiply(X2,multiply(X1,X3)),associator(X2,X1,X3)),add(additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X2,multiply(X1,X3)))),multiply(X0,multiply(X1,X3))))),
inference(backward_demodulation,[],[f1144,f1680]) ).
fof(f1749,plain,
! [X2,X3,X0,X1] : add(X3,add(X0,add(X1,X2))) = add(X0,add(X1,add(X3,X2))),
inference(forward_demodulation,[],[f1609,f15]) ).
fof(f1752,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X2,multiply(X1,X3)),add(associator(X2,X1,X3),add(additive_inverse(add(multiply(X0,multiply(X1,X3)),multiply(X2,multiply(X1,X3)))),multiply(X0,multiply(X1,X3)))))),
inference(forward_demodulation,[],[f1687,f15]) ).
fof(f1779,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),add(multiply(x,multiply(y,multiply(z,x))),add(additive_inverse(multiply(x,associator(y,z,x))),additive_inverse(multiply(x,multiply(y,multiply(z,x)))))))),
inference(backward_demodulation,[],[f1274,f1749]) ).
fof(f1791,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),add(multiply(X2,multiply(X1,X3)),add(associator(X2,X1,X3),additive_inverse(multiply(X2,multiply(X1,X3)))))),
inference(forward_demodulation,[],[f1752,f363]) ).
fof(f1804,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(x,y,multiply(z,x)),add(associator(multiply(x,y),z,x),additive_inverse(multiply(x,associator(y,z,x))))),
inference(forward_demodulation,[],[f1779,f302]) ).
fof(f1805,plain,
! [X2,X3,X0,X1] : associator(add(X0,X2),X1,X3) = add(associator(X0,X1,X3),associator(X2,X1,X3)),
inference(forward_demodulation,[],[f1791,f302]) ).
fof(f1807,plain,
! [X2,X0,X1] : additive_identity = add(add(associator(X0,X0,X2),associator(X1,X0,X2)),associator(add(X0,X1),X1,X2)),
inference(backward_demodulation,[],[f551,f1805]) ).
fof(f1823,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X0,X2),add(associator(X1,X0,X2),associator(add(X0,X1),X1,X2))),
inference(forward_demodulation,[],[f1807,f15]) ).
fof(f1830,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X0,X2),add(associator(X1,X0,X2),add(associator(X0,X1,X2),associator(X1,X1,X2)))),
inference(forward_demodulation,[],[f1823,f1805]) ).
fof(f1837,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X0,X2),add(associator(X1,X0,X2),add(associator(X0,X1,X2),additive_identity))),
inference(forward_demodulation,[],[f1830,f104]) ).
fof(f1844,plain,
! [X2,X0,X1] : additive_identity = add(associator(X0,X0,X2),add(associator(X1,X0,X2),associator(X0,X1,X2))),
inference(forward_demodulation,[],[f1837,f2]) ).
fof(f1851,plain,
! [X2,X0,X1] : additive_identity = add(additive_identity,add(associator(X1,X0,X2),associator(X0,X1,X2))),
inference(forward_demodulation,[],[f1844,f104]) ).
fof(f1858,plain,
! [X2,X0,X1] : additive_identity = add(associator(X1,X0,X2),associator(X0,X1,X2)),
inference(forward_demodulation,[],[f1851,f1]) ).
fof(f1890,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(multiply(x,y),z,x),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))),
inference(superposition,[],[f1804,f192]) ).
fof(f1934,plain,
! [X2,X0,X1] : associator(X1,X0,X2) = add(additive_inverse(associator(X0,X1,X2)),additive_identity),
inference(superposition,[],[f286,f1858]) ).
fof(f1939,plain,
! [X2,X0,X1] : associator(X1,X0,X2) = additive_inverse(associator(X0,X1,X2)),
inference(forward_demodulation,[],[f1934,f2]) ).
fof(f1960,plain,
! [X2,X0,X1] : add(multiply(X0,multiply(X1,multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),additive_inverse(add(multiply(X0,multiply(X1,multiply(X1,X2))),associator(X0,X1,multiply(X1,X2)))))) = additive_inverse(associator(X1,multiply(X0,X1),X2)),
inference(backward_demodulation,[],[f1009,f1939]) ).
fof(f1971,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(z,multiply(x,y),x)),add(additive_inverse(multiply(x,associator(y,z,x))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f1890,f1939]) ).
fof(f2027,plain,
! [X2,X0,X1] : additive_identity = add(associator(X1,X2,X0),additive_inverse(associator(X0,X1,X2))),
inference(superposition,[],[f573,f1939]) ).
fof(f2034,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X1,X2,X0),
inference(superposition,[],[f847,f1939]) ).
fof(f2054,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(z,multiply(x,y),x)),add(additive_inverse(multiply(x,associator(x,y,z))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f1971,f2034]) ).
fof(f2085,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(z,multiply(x,y),x)),add(additive_inverse(add(additive_inverse(associator(x,multiply(x,y),z)),associator(multiply(x,x),y,z))),associator(x,y,multiply(z,x)))),
inference(forward_demodulation,[],[f2054,f1316]) ).
fof(f2134,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X2,X1,X0)),
inference(superposition,[],[f1939,f2034]) ).
fof(f2145,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(z,multiply(x,y),x)),add(additive_inverse(add(additive_inverse(associator(x,multiply(x,y),z)),additive_inverse(associator(z,y,multiply(x,x))))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f2085,f2134]) ).
fof(f2596,plain,
! [X2,X0,X1] : additive_inverse(associator(X0,X1,X2)) = additive_inverse(associator(additive_inverse(X2),X1,X0)),
inference(superposition,[],[f2134,f1171]) ).
fof(f2609,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(additive_inverse(x),multiply(x,y),z)),add(additive_inverse(add(additive_inverse(associator(x,multiply(x,y),z)),additive_inverse(associator(z,y,multiply(x,x))))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f2145,f2596]) ).
fof(f2859,plain,
! [X0,X1] : add(X1,additive_inverse(add(X0,X1))) = add(additive_inverse(X0),additive_identity),
inference(superposition,[],[f283,f266]) ).
fof(f2874,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(forward_demodulation,[],[f2859,f2]) ).
fof(f2950,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(superposition,[],[f283,f2874]) ).
fof(f2956,plain,
! [X0,X1] : add(X1,additive_inverse(X0)) = additive_inverse(add(X0,additive_inverse(X1))),
inference(superposition,[],[f271,f2874]) ).
fof(f2965,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(additive_inverse(x),multiply(x,y),z)),add(add(associator(z,y,multiply(x,x)),additive_inverse(additive_inverse(associator(x,multiply(x,y),z)))),associator(x,y,multiply(z,x)))),
inference(backward_demodulation,[],[f2609,f2956]) ).
fof(f2990,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = add(multiply(X0,multiply(X1,X2)),add(additive_inverse(associator(X0,X1,X2)),additive_inverse(multiply(X0,multiply(X1,X2))))),
inference(backward_demodulation,[],[f1108,f2950]) ).
fof(f2991,plain,
! [X2,X0,X1] : additive_inverse(associator(X1,multiply(X0,X1),X2)) = add(multiply(X0,multiply(X1,multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),add(additive_inverse(associator(X0,X1,multiply(X1,X2))),additive_inverse(multiply(X0,multiply(X1,multiply(X1,X2))))))),
inference(backward_demodulation,[],[f1960,f2950]) ).
fof(f3038,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(additive_inverse(x),multiply(x,y),z)),add(associator(z,y,multiply(x,x)),add(additive_inverse(additive_inverse(associator(x,multiply(x,y),z))),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f2965,f15]) ).
fof(f3061,plain,
! [X2,X0,X1] : additive_inverse(associator(X1,multiply(X0,X1),X2)) = add(associator(X0,multiply(X1,X1),X2),additive_inverse(associator(X0,X1,multiply(X1,X2)))),
inference(forward_demodulation,[],[f2991,f415]) ).
fof(f3062,plain,
! [X2,X0,X1] : associator(additive_inverse(X0),X1,X2) = additive_inverse(associator(X0,X1,X2)),
inference(forward_demodulation,[],[f2990,f302]) ).
fof(f3094,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(additive_inverse(x),multiply(x,y),z)),add(associator(z,y,multiply(x,x)),add(associator(x,multiply(x,y),z),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f3038,f11]) ).
fof(f3148,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(additive_inverse(associator(x,multiply(x,y),z))),add(associator(z,y,multiply(x,x)),add(associator(x,multiply(x,y),z),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f3094,f3062]) ).
fof(f3187,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(associator(x,multiply(x,y),z),add(associator(z,y,multiply(x,x)),add(associator(x,multiply(x,y),z),associator(x,y,multiply(z,x))))),
inference(forward_demodulation,[],[f3148,f11]) ).
fof(f4010,plain,
! [X2,X3,X0,X1,X4] : add(X4,X0) = add(associator(X1,X2,X3),add(X4,add(associator(X1,X3,X2),X0))),
inference(superposition,[],[f200,f849]) ).
fof(f4011,plain,
! [X2,X3,X0,X1] : add(associator(X1,X3,X2),X0) = add(additive_inverse(associator(X1,X2,X3)),X0),
inference(superposition,[],[f283,f849]) ).
fof(f4022,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(associator(z,y,multiply(x,x)),add(associator(x,multiply(x,y),z),associator(x,y,multiply(z,x))))),
inference(backward_demodulation,[],[f3187,f4011]) ).
fof(f5651,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),additive_inverse(associator(X0,X1,multiply(X1,X2)))),
inference(superposition,[],[f847,f3061]) ).
fof(f5705,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(associator(z,y,multiply(x,x)),add(associator(x,multiply(x,y),z),add(associator(z,multiply(x,x),y),additive_inverse(associator(z,x,multiply(x,y))))))),
inference(backward_demodulation,[],[f4022,f5651]) ).
fof(f5795,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),add(associator(x,multiply(x,y),z),additive_inverse(associator(z,x,multiply(x,y))))),
inference(forward_demodulation,[],[f5705,f4010]) ).
fof(f5860,plain,
additive_inverse(associator(x,z,multiply(x,y))) != add(additive_inverse(associator(x,z,multiply(x,y))),additive_identity),
inference(forward_demodulation,[],[f5795,f2027]) ).
fof(f5922,plain,
$false,
inference(forward_subsumption_resolution,[],[f5860,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG027-8 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 % Computer : n011.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sun Sep 27 23:00:16 UTC 2026
% 0.16/0.46 % CPUTime :
% 0.16/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.66/8.38 % (2863959)Detected a unit-equality problem, will run specialized UEQ schedule.
% 52.66/8.38 % (2863977)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1173041602:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 52.66/8.38 % (2863975)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4055718707:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 52.66/8.38 % (2863974)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=308110802:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 52.66/8.38 % (2863973)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2048132797:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 52.66/8.38 % (2863972)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1862465015:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 52.66/8.38 % (2863978)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3778061298:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 52.66/8.38 % (2863976)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2399922653:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 52.66/8.38 % (2863977)Instruction limit reached!
% 52.66/8.38 % (2863977)------------------------------
% 52.66/8.38 % (2863977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863977)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863977)Termination reason: Instruction limit
% 52.66/8.38 % (2863977)Termination phase: Saturation
% 52.66/8.38 % (2863977)Time elapsed: 0.140 s
% 52.66/8.38 % (2863977)Peak memory usage: 90 MB
% 52.66/8.38 % (2863977)Instructions burned: 258 (million)
% 52.66/8.38 % (2863975)Instruction limit reached!
% 52.66/8.38 % (2863975)------------------------------
% 52.66/8.38 % (2863975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863975)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863975)Termination reason: Instruction limit
% 52.66/8.38 % (2863975)Termination phase: Saturation
% 52.66/8.38 % (2863975)Time elapsed: 0.112 s
% 52.66/8.38 % (2863975)Peak memory usage: 88 MB
% 52.66/8.38 % (2863975)Instructions burned: 137 (million)
% 52.66/8.38 % (2863976)Instruction limit reached!
% 52.66/8.38 % (2863976)------------------------------
% 52.66/8.38 % (2863976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863976)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863976)Termination reason: Instruction limit
% 52.66/8.38 % (2863976)Termination phase: Saturation
% 52.66/8.38 % (2863976)Time elapsed: 0.174 s
% 52.66/8.38 % (2863976)Peak memory usage: 89 MB
% 52.66/8.38 % (2863976)Instructions burned: 181 (million)
% 52.66/8.38 % (2863986)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3395845297:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 52.66/8.38 % (2863987)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=384448092:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 52.66/8.38 % (2863988)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3400543641:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 52.66/8.38 % (2863988)Instruction limit reached!
% 52.66/8.38 % (2863988)------------------------------
% 52.66/8.38 % (2863988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863988)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863988)Termination reason: Instruction limit
% 52.66/8.38 % (2863988)Termination phase: Saturation
% 52.66/8.38 % (2863988)Time elapsed: 0.175 s
% 52.66/8.38 % (2863988)Peak memory usage: 89 MB
% 52.66/8.38 % (2863988)Instructions burned: 216 (million)
% 52.66/8.38 % (2863994)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1114959281:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 52.66/8.38 % (2863978)Instruction limit reached!
% 52.66/8.38 % (2863978)------------------------------
% 52.66/8.38 % (2863978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863978)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863978)Termination reason: Instruction limit
% 52.66/8.38 % (2863978)Termination phase: Saturation
% 52.66/8.38 % (2863978)Time elapsed: 1.047 s
% 52.66/8.38 % (2863978)Peak memory usage: 96 MB
% 52.66/8.38 % (2863978)Instructions burned: 1187 (million)
% 52.66/8.38 % (2863994)Instruction limit reached!
% 52.66/8.38 % (2863994)------------------------------
% 52.66/8.38 % (2863994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863994)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863994)Termination reason: Instruction limit
% 52.66/8.38 % (2863994)Termination phase: Saturation
% 52.66/8.38 % (2863994)Time elapsed: 0.315 s
% 52.66/8.38 % (2863994)Peak memory usage: 93 MB
% 52.66/8.38 % (2863994)Instructions burned: 317 (million)
% 52.66/8.38 % (2863996)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3364127692:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 52.66/8.38 % (2863997)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2365484423:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 52.66/8.38 % (2863986)Instruction limit reached!
% 52.66/8.38 % (2863986)------------------------------
% 52.66/8.38 % (2863986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863986)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863986)Termination reason: Instruction limit
% 52.66/8.38 % (2863986)Termination phase: Saturation
% 52.66/8.38 % (2863986)Time elapsed: 1.210 s
% 52.66/8.38 % (2863986)Peak memory usage: 141 MB
% 52.66/8.38 % (2863986)Instructions burned: 2052 (million)
% 52.66/8.38 % (2864000)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=513539867:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2983 on theBenchmark for (2983ds/14534Mi)
% 52.66/8.38 % (2863997)Instruction limit reached!
% 52.66/8.38 % (2863997)------------------------------
% 52.66/8.38 % (2863997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863997)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863997)Termination reason: Instruction limit
% 52.66/8.38 % (2863997)Termination phase: Saturation
% 52.66/8.38 % (2863997)Time elapsed: 2.902 s
% 52.66/8.38 % (2863997)Peak memory usage: 119 MB
% 52.66/8.38 % (2863997)Instructions burned: 2836 (million)
% 52.66/8.38 % (2864004)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=4287539647:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2955 on theBenchmark for (2955ds/11832Mi)
% 52.66/8.38 % (2863987)Instruction limit reached!
% 52.66/8.38 % (2863987)------------------------------
% 52.66/8.38 % (2863987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 52.66/8.38 % (2863987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 52.66/8.38 % (2863987)CaDiCaL version: 2.1.3
% 52.66/8.38 % (2863987)Termination reason: Instruction limit
% 52.66/8.38 % (2863987)Termination phase: Saturation
% 52.66/8.38 % (2863987)Time elapsed: 4.999 s
% 52.66/8.38 % (2863987)Peak memory usage: 167 MB
% 52.66/8.38 % (2863987)Instructions burned: 4948 (million)
% 52.66/8.38 % (2864008)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=2413110359:i=2279:fgj=on:bd=all_2944 on theBenchmark for (2944ds/2279Mi)
% 52.66/8.38 % (2864008)First to succeed.
% 52.66/8.38 % (2864008)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2863959"
% 52.66/8.38 % (2864008)Refutation found. Thanks to Tanya!
% 52.66/8.38 % SZS status Unsatisfiable for theBenchmark
% 52.66/8.38 % SZS output start Proof for theBenchmark
% See solution above
% 53.43/8.66 % (2864008)------------------------------
% 53.43/8.66 % (2864008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 53.43/8.66 % (2864008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 53.43/8.66 % (2864008)CaDiCaL version: 2.1.3
% 53.43/8.66 % (2864008)Termination reason: Refutation
% 53.43/8.66 % (2864008)Time elapsed: 1.354 s
% 53.43/8.66 % (2864008)Peak memory usage: 133 MB
% 53.43/8.66 % (2864008)Instructions burned: 1671 (million)
% 53.43/8.66 % (2864008)------------------------------
% 53.43/8.66 % (2864008)------------------------------
% 53.43/8.66 % (2863959)Success in time 7.419 s
% 53.43/8.66 % Vampire exiting
%------------------------------------------------------------------------------