TSTP Solution File: RNG009-5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n010.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 : Thu Aug 31 13:59:34 EDT 2023
% Result : Unsatisfiable 3.52s 0.90s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 11
% Syntax : Number of formulae : 208 ( 208 unt; 0 def)
% Number of atoms : 208 ( 207 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 231 (; 231 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16924,plain,
$false,
inference(subsumption_resolution,[],[f16923,f12]) ).
fof(f12,plain,
sF0 != sF1,
inference(definition_folding,[],[f9,f11,f10]) ).
fof(f10,plain,
multiply(a,b) = sF0,
introduced(function_definition,[]) ).
fof(f11,plain,
multiply(b,a) = sF1,
introduced(function_definition,[]) ).
fof(f9,axiom,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',prove_commutativity) ).
fof(f16923,plain,
sF0 = sF1,
inference(forward_demodulation,[],[f16756,f1]) ).
fof(f1,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',right_identity) ).
fof(f16756,plain,
sF1 = add(sF0,additive_identity),
inference(superposition,[],[f44,f16353]) ).
fof(f16353,plain,
additive_identity = add(sF1,additive_inverse(sF0)),
inference(forward_demodulation,[],[f16352,f2220]) ).
fof(f2220,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(superposition,[],[f2200,f55]) ).
fof(f55,plain,
! [X7] : additive_inverse(additive_inverse(X7)) = X7,
inference(forward_demodulation,[],[f48,f1]) ).
fof(f48,plain,
! [X7] : additive_inverse(additive_inverse(X7)) = add(X7,additive_identity),
inference(superposition,[],[f38,f2]) ).
fof(f2,axiom,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',right_additive_inverse) ).
fof(f38,plain,
! [X2,X3] : add(X2,add(additive_inverse(X2),X3)) = X3,
inference(forward_demodulation,[],[f25,f13]) ).
fof(f13,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f6,f1]) ).
fof(f6,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',commutative_addition) ).
fof(f25,plain,
! [X2,X3] : add(X2,add(additive_inverse(X2),X3)) = add(additive_identity,X3),
inference(superposition,[],[f5,f2]) ).
fof(f5,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',associative_addition) ).
fof(f2200,plain,
! [X35] : additive_identity = multiply(additive_inverse(X35),additive_identity),
inference(forward_demodulation,[],[f2181,f2]) ).
fof(f2181,plain,
! [X35] : multiply(additive_inverse(X35),additive_identity) = add(X35,additive_inverse(X35)),
inference(superposition,[],[f38,f2126]) ).
fof(f2126,plain,
! [X8] : add(X8,multiply(X8,additive_identity)) = X8,
inference(forward_demodulation,[],[f2074,f8]) ).
fof(f8,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = X0,
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',x_cubed_is_x) ).
fof(f2074,plain,
! [X8] : add(X8,multiply(X8,additive_identity)) = multiply(X8,multiply(X8,X8)),
inference(superposition,[],[f238,f1]) ).
fof(f238,plain,
! [X0,X1] : multiply(X0,add(multiply(X0,X0),X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[],[f3,f8]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',distribute1) ).
fof(f16352,plain,
multiply(b,additive_identity) = add(sF1,additive_inverse(sF0)),
inference(backward_demodulation,[],[f14566,f16351]) ).
fof(f16351,plain,
additive_identity = multiply(b,add(sF1,additive_inverse(sF0))),
inference(forward_demodulation,[],[f16350,f17]) ).
fof(f17,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f13,f2]) ).
fof(f16350,plain,
additive_inverse(additive_identity) = multiply(b,add(sF1,additive_inverse(sF0))),
inference(forward_demodulation,[],[f16310,f216]) ).
fof(f216,plain,
! [X14,X13] : additive_inverse(add(X14,additive_inverse(X13))) = add(X13,additive_inverse(X14)),
inference(superposition,[],[f38,f160]) ).
fof(f160,plain,
! [X2,X1] : additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(superposition,[],[f158,f55]) ).
fof(f158,plain,
! [X12,X13] : add(X13,additive_inverse(add(additive_inverse(X12),X13))) = X12,
inference(forward_demodulation,[],[f136,f1]) ).
fof(f136,plain,
! [X12,X13] : add(X13,additive_inverse(add(additive_inverse(X12),X13))) = add(X12,additive_identity),
inference(superposition,[],[f38,f31]) ).
fof(f31,plain,
! [X6,X5] : additive_identity = add(X5,add(X6,additive_inverse(add(X5,X6)))),
inference(superposition,[],[f5,f2]) ).
fof(f16310,plain,
additive_inverse(additive_identity) = multiply(b,additive_inverse(add(sF0,additive_inverse(sF1)))),
inference(superposition,[],[f11060,f16092]) ).
fof(f16092,plain,
additive_identity = multiply(b,add(sF0,additive_inverse(sF1))),
inference(forward_demodulation,[],[f16091,f2220]) ).
fof(f16091,plain,
multiply(b,additive_identity) = multiply(b,add(sF0,additive_inverse(sF1))),
inference(forward_demodulation,[],[f16057,f15214]) ).
fof(f15214,plain,
! [X4] : additive_identity = multiply(add(sF0,additive_inverse(sF1)),multiply(b,X4)),
inference(forward_demodulation,[],[f15193,f7294]) ).
fof(f7294,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(forward_demodulation,[],[f7293,f1]) ).
fof(f7293,plain,
! [X0] : additive_identity = multiply(additive_identity,add(X0,additive_identity)),
inference(forward_demodulation,[],[f7276,f2220]) ).
fof(f7276,plain,
! [X0] : additive_identity = multiply(additive_identity,add(X0,multiply(X0,additive_identity))),
inference(backward_demodulation,[],[f2391,f7275]) ).
fof(f7275,plain,
! [X13] : additive_identity = additive_inverse(multiply(additive_identity,X13)),
inference(forward_demodulation,[],[f7212,f2]) ).
fof(f7212,plain,
! [X13] : add(X13,additive_inverse(X13)) = additive_inverse(multiply(additive_identity,X13)),
inference(superposition,[],[f201,f7114]) ).
fof(f7114,plain,
! [X14] : add(X14,multiply(additive_identity,X14)) = X14,
inference(forward_demodulation,[],[f7113,f8]) ).
fof(f7113,plain,
! [X14] : multiply(X14,multiply(X14,X14)) = add(X14,multiply(additive_identity,X14)),
inference(forward_demodulation,[],[f7042,f7]) ).
fof(f7,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',associative_multiplication) ).
fof(f7042,plain,
! [X14] : multiply(multiply(X14,X14),X14) = add(X14,multiply(additive_identity,X14)),
inference(superposition,[],[f6411,f1]) ).
fof(f6411,plain,
! [X0,X1] : multiply(add(multiply(X0,X0),X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[],[f661,f8]) ).
fof(f661,plain,
! [X8,X6,X7,X5] : multiply(add(multiply(X5,X6),X8),X7) = add(multiply(X5,multiply(X6,X7)),multiply(X8,X7)),
inference(superposition,[],[f4,f7]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115',distribute2) ).
fof(f201,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
inference(superposition,[],[f160,f6]) ).
fof(f2391,plain,
! [X0] : additive_identity = multiply(additive_identity,add(X0,multiply(X0,additive_inverse(multiply(additive_identity,X0))))),
inference(forward_demodulation,[],[f2390,f2339]) ).
fof(f2339,plain,
! [X2,X3] : multiply(additive_identity,multiply(X2,add(multiply(additive_identity,X2),X3))) = multiply(additive_identity,add(X2,multiply(X2,X3))),
inference(forward_demodulation,[],[f2338,f3]) ).
fof(f2338,plain,
! [X2,X3] : multiply(additive_identity,multiply(X2,add(multiply(additive_identity,X2),X3))) = add(multiply(additive_identity,X2),multiply(additive_identity,multiply(X2,X3))),
inference(forward_demodulation,[],[f2337,f7]) ).
fof(f2337,plain,
! [X2,X3] : add(multiply(additive_identity,X2),multiply(multiply(additive_identity,X2),X3)) = multiply(additive_identity,multiply(X2,add(multiply(additive_identity,X2),X3))),
inference(forward_demodulation,[],[f2313,f7]) ).
fof(f2313,plain,
! [X2,X3] : add(multiply(additive_identity,X2),multiply(multiply(additive_identity,X2),X3)) = multiply(multiply(additive_identity,X2),add(multiply(additive_identity,X2),X3)),
inference(superposition,[],[f238,f2259]) ).
fof(f2259,plain,
! [X10,X11] : multiply(additive_identity,X11) = multiply(X10,multiply(additive_identity,X11)),
inference(superposition,[],[f7,f2220]) ).
fof(f2390,plain,
! [X0] : additive_identity = multiply(additive_identity,multiply(X0,add(multiply(additive_identity,X0),additive_inverse(multiply(additive_identity,X0))))),
inference(forward_demodulation,[],[f2389,f7]) ).
fof(f2389,plain,
! [X0] : additive_identity = multiply(multiply(additive_identity,X0),add(multiply(additive_identity,X0),additive_inverse(multiply(additive_identity,X0)))),
inference(forward_demodulation,[],[f2363,f2319]) ).
fof(f2319,plain,
! [X18,X16,X17] : multiply(X16,add(multiply(additive_identity,X17),X18)) = add(multiply(additive_identity,X17),multiply(X16,X18)),
inference(superposition,[],[f3,f2259]) ).
fof(f2363,plain,
! [X0] : additive_identity = add(multiply(additive_identity,X0),multiply(multiply(additive_identity,X0),additive_inverse(multiply(additive_identity,X0)))),
inference(superposition,[],[f2236,f2259]) ).
fof(f2236,plain,
! [X37] : additive_identity = add(X37,multiply(X37,additive_inverse(multiply(X37,X37)))),
inference(backward_demodulation,[],[f2085,f2220]) ).
fof(f2085,plain,
! [X37] : add(X37,multiply(X37,additive_inverse(multiply(X37,X37)))) = multiply(X37,additive_identity),
inference(superposition,[],[f238,f2]) ).
fof(f15193,plain,
! [X4] : multiply(additive_identity,X4) = multiply(add(sF0,additive_inverse(sF1)),multiply(b,X4)),
inference(superposition,[],[f7,f15165]) ).
fof(f15165,plain,
additive_identity = multiply(add(sF0,additive_inverse(sF1)),b),
inference(forward_demodulation,[],[f15164,f11924]) ).
fof(f11924,plain,
additive_inverse(sF1) = multiply(b,additive_inverse(a)),
inference(superposition,[],[f11060,f11]) ).
fof(f15164,plain,
additive_identity = multiply(add(sF0,multiply(b,additive_inverse(a))),b),
inference(forward_demodulation,[],[f15163,f12789]) ).
fof(f12789,plain,
! [X14,X13] : multiply(X13,additive_inverse(X14)) = multiply(additive_inverse(X13),X14),
inference(superposition,[],[f12586,f55]) ).
fof(f12586,plain,
! [X10,X8] : multiply(X8,X10) = multiply(additive_inverse(X8),additive_inverse(X10)),
inference(forward_demodulation,[],[f12585,f11483]) ).
fof(f11483,plain,
! [X14,X12,X13] : multiply(X12,additive_inverse(X13)) = add(multiply(X14,X13),multiply(add(X12,X14),additive_inverse(X13))),
inference(forward_demodulation,[],[f11123,f11060]) ).
fof(f11123,plain,
! [X14,X12,X13] : add(multiply(X14,X13),additive_inverse(multiply(add(X12,X14),X13))) = multiply(X12,additive_inverse(X13)),
inference(backward_demodulation,[],[f696,f11060]) ).
fof(f696,plain,
! [X14,X12,X13] : additive_inverse(multiply(X12,X13)) = add(multiply(X14,X13),additive_inverse(multiply(add(X12,X14),X13))),
inference(superposition,[],[f160,f4]) ).
fof(f12585,plain,
! [X10,X8,X9] : multiply(X8,X10) = add(multiply(X9,X10),multiply(add(additive_inverse(X8),X9),additive_inverse(X10))),
inference(forward_demodulation,[],[f12507,f6]) ).
fof(f12507,plain,
! [X10,X8,X9] : multiply(X8,X10) = add(multiply(add(additive_inverse(X8),X9),additive_inverse(X10)),multiply(X9,X10)),
inference(superposition,[],[f11139,f38]) ).
fof(f11139,plain,
! [X98,X99,X97] : multiply(X99,X98) = add(multiply(X97,additive_inverse(X98)),multiply(add(X99,X97),X98)),
inference(backward_demodulation,[],[f9722,f11060]) ).
fof(f9722,plain,
! [X98,X99,X97] : multiply(X99,X98) = add(additive_inverse(multiply(X97,X98)),multiply(add(X99,X97),X98)),
inference(forward_demodulation,[],[f9721,f6]) ).
fof(f9721,plain,
! [X98,X99,X97] : multiply(X99,X98) = add(multiply(add(X99,X97),X98),additive_inverse(multiply(X97,X98))),
inference(forward_demodulation,[],[f9269,f1]) ).
fof(f9269,plain,
! [X98,X99,X97] : add(multiply(add(X99,X97),X98),additive_inverse(multiply(X97,X98))) = add(multiply(X99,X98),additive_identity),
inference(superposition,[],[f693,f2]) ).
fof(f693,plain,
! [X2,X3,X4,X5] : add(multiply(X2,X3),add(multiply(X4,X3),X5)) = add(multiply(add(X2,X4),X3),X5),
inference(superposition,[],[f5,f4]) ).
fof(f15163,plain,
additive_identity = multiply(add(sF0,multiply(additive_inverse(b),a)),b),
inference(backward_demodulation,[],[f13304,f15162]) ).
fof(f15162,plain,
! [X0] : multiply(add(sF0,multiply(X0,a)),b) = multiply(add(X0,multiply(a,sF0)),sF0),
inference(forward_demodulation,[],[f15161,f736]) ).
fof(f736,plain,
! [X6,X7,X5] : multiply(add(X5,X7),X6) = multiply(add(X7,X5),X6),
inference(forward_demodulation,[],[f690,f4]) ).
fof(f690,plain,
! [X6,X7,X5] : add(multiply(X7,X6),multiply(X5,X6)) = multiply(add(X5,X7),X6),
inference(superposition,[],[f4,f6]) ).
fof(f15161,plain,
! [X0] : multiply(add(multiply(X0,a),sF0),b) = multiply(add(X0,multiply(a,sF0)),sF0),
inference(forward_demodulation,[],[f15129,f6350]) ).
fof(f6350,plain,
! [X114,X115] : multiply(add(multiply(X114,a),X115),b) = add(multiply(X114,sF0),multiply(X115,b)),
inference(superposition,[],[f661,f10]) ).
fof(f15129,plain,
! [X0] : add(multiply(X0,sF0),multiply(sF0,b)) = multiply(add(X0,multiply(a,sF0)),sF0),
inference(superposition,[],[f676,f14512]) ).
fof(f14512,plain,
multiply(sF0,b) = multiply(a,multiply(sF0,sF0)),
inference(forward_demodulation,[],[f14511,f14504]) ).
fof(f14504,plain,
! [X6] : multiply(a,multiply(sF0,X6)) = multiply(sF0,multiply(b,multiply(sF0,X6))),
inference(forward_demodulation,[],[f14503,f7]) ).
fof(f14503,plain,
! [X6] : multiply(a,multiply(sF0,X6)) = multiply(sF0,multiply(multiply(b,sF0),X6)),
inference(forward_demodulation,[],[f14479,f7]) ).
fof(f14479,plain,
! [X6] : multiply(sF0,multiply(multiply(b,sF0),X6)) = multiply(multiply(a,sF0),X6),
inference(superposition,[],[f7,f14424]) ).
fof(f14424,plain,
multiply(a,sF0) = multiply(sF0,multiply(b,sF0)),
inference(superposition,[],[f66,f14391]) ).
fof(f14391,plain,
sF0 = multiply(b,multiply(b,sF0)),
inference(forward_demodulation,[],[f14390,f106]) ).
fof(f106,plain,
multiply(sF1,b) = multiply(b,sF0),
inference(superposition,[],[f67,f10]) ).
fof(f67,plain,
! [X7] : multiply(b,multiply(a,X7)) = multiply(sF1,X7),
inference(superposition,[],[f7,f11]) ).
fof(f14390,plain,
sF0 = multiply(b,multiply(sF1,b)),
inference(forward_demodulation,[],[f14389,f1]) ).
fof(f14389,plain,
multiply(b,multiply(sF1,b)) = add(sF0,additive_identity),
inference(forward_demodulation,[],[f14388,f7]) ).
fof(f14388,plain,
add(sF0,additive_identity) = multiply(multiply(b,sF1),b),
inference(forward_demodulation,[],[f14370,f38]) ).
fof(f14370,plain,
add(sF0,additive_identity) = multiply(add(a,add(additive_inverse(a),multiply(b,sF1))),b),
inference(superposition,[],[f662,f13302]) ).
fof(f13302,plain,
additive_identity = multiply(add(additive_inverse(a),multiply(b,sF1)),b),
inference(backward_demodulation,[],[f11395,f13297]) ).
fof(f13297,plain,
! [X50,X51,X52,X53] : multiply(add(additive_inverse(X50),multiply(X52,X53)),X51) = multiply(add(X50,multiply(X52,additive_inverse(X53))),additive_inverse(X51)),
inference(forward_demodulation,[],[f13164,f12819]) ).
fof(f12819,plain,
! [X54,X55,X52,X53] : multiply(add(X54,multiply(X55,additive_inverse(X52))),additive_inverse(X53)) = add(multiply(X54,additive_inverse(X53)),multiply(X55,multiply(X52,X53))),
inference(superposition,[],[f676,f12586]) ).
fof(f13164,plain,
! [X50,X51,X52,X53] : multiply(add(additive_inverse(X50),multiply(X52,X53)),X51) = add(multiply(X50,additive_inverse(X51)),multiply(X52,multiply(X53,X51))),
inference(superposition,[],[f676,f12789]) ).
fof(f11395,plain,
additive_identity = multiply(add(a,multiply(b,additive_inverse(sF1))),additive_inverse(b)),
inference(backward_demodulation,[],[f8933,f11060]) ).
fof(f8933,plain,
additive_identity = multiply(add(a,additive_inverse(multiply(b,sF1))),additive_inverse(b)),
inference(superposition,[],[f7873,f2414]) ).
fof(f2414,plain,
! [X12] : additive_inverse(X12) = multiply(X12,additive_inverse(multiply(X12,X12))),
inference(forward_demodulation,[],[f2413,f13]) ).
fof(f2413,plain,
! [X12] : additive_inverse(X12) = add(additive_identity,multiply(X12,additive_inverse(multiply(X12,X12)))),
inference(forward_demodulation,[],[f2412,f17]) ).
fof(f2412,plain,
! [X12] : additive_inverse(X12) = add(additive_inverse(additive_identity),multiply(X12,additive_inverse(multiply(X12,X12)))),
inference(forward_demodulation,[],[f2380,f6]) ).
fof(f2380,plain,
! [X12] : additive_inverse(X12) = add(multiply(X12,additive_inverse(multiply(X12,X12))),additive_inverse(additive_identity)),
inference(superposition,[],[f160,f2236]) ).
fof(f7873,plain,
! [X4] : additive_identity = multiply(add(a,additive_inverse(multiply(b,sF1))),multiply(b,X4)),
inference(forward_demodulation,[],[f7859,f7294]) ).
fof(f7859,plain,
! [X4] : multiply(additive_identity,X4) = multiply(add(a,additive_inverse(multiply(b,sF1))),multiply(b,X4)),
inference(superposition,[],[f7,f7826]) ).
fof(f7826,plain,
additive_identity = multiply(add(a,additive_inverse(multiply(b,sF1))),b),
inference(forward_demodulation,[],[f7825,f2220]) ).
fof(f7825,plain,
multiply(add(a,additive_inverse(multiply(b,sF1))),additive_identity) = multiply(add(a,additive_inverse(multiply(b,sF1))),b),
inference(forward_demodulation,[],[f7785,f7309]) ).
fof(f7309,plain,
! [X4] : additive_identity = multiply(b,multiply(add(a,additive_inverse(multiply(b,sF1))),X4)),
inference(backward_demodulation,[],[f6287,f7294]) ).
fof(f6287,plain,
! [X4] : multiply(additive_identity,X4) = multiply(b,multiply(add(a,additive_inverse(multiply(b,sF1))),X4)),
inference(superposition,[],[f7,f6242]) ).
fof(f6242,plain,
additive_identity = multiply(b,add(a,additive_inverse(multiply(b,sF1)))),
inference(forward_demodulation,[],[f6203,f2220]) ).
fof(f6203,plain,
multiply(b,additive_identity) = multiply(b,add(a,additive_inverse(multiply(b,sF1)))),
inference(superposition,[],[f627,f2]) ).
fof(f627,plain,
! [X1] : multiply(b,add(multiply(b,sF1),X1)) = multiply(b,add(a,X1)),
inference(forward_demodulation,[],[f623,f242]) ).
fof(f242,plain,
! [X9] : multiply(b,add(a,X9)) = add(sF1,multiply(b,X9)),
inference(superposition,[],[f3,f11]) ).
fof(f623,plain,
! [X1] : multiply(b,add(multiply(b,sF1),X1)) = add(sF1,multiply(b,X1)),
inference(superposition,[],[f3,f578]) ).
fof(f578,plain,
sF1 = multiply(b,multiply(b,sF1)),
inference(superposition,[],[f71,f11]) ).
fof(f71,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,multiply(X0,X1))),
inference(forward_demodulation,[],[f64,f7]) ).
fof(f64,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(multiply(X0,X0),X1)),
inference(superposition,[],[f7,f8]) ).
fof(f7785,plain,
multiply(add(a,additive_inverse(multiply(b,sF1))),multiply(b,multiply(add(a,additive_inverse(multiply(b,sF1))),additive_identity))) = multiply(add(a,additive_inverse(multiply(b,sF1))),b),
inference(superposition,[],[f74,f7309]) ).
fof(f74,plain,
! [X3,X4] : multiply(X3,X4) = multiply(X3,multiply(X4,multiply(X3,multiply(X4,multiply(X3,X4))))),
inference(forward_demodulation,[],[f68,f7]) ).
fof(f68,plain,
! [X3,X4] : multiply(X3,X4) = multiply(X3,multiply(X4,multiply(multiply(X3,X4),multiply(X3,X4)))),
inference(superposition,[],[f7,f8]) ).
fof(f662,plain,
! [X9] : multiply(add(a,X9),b) = add(sF0,multiply(X9,b)),
inference(superposition,[],[f4,f10]) ).
fof(f66,plain,
! [X6] : multiply(a,multiply(b,X6)) = multiply(sF0,X6),
inference(superposition,[],[f7,f10]) ).
fof(f14511,plain,
multiply(sF0,b) = multiply(sF0,multiply(b,multiply(sF0,sF0))),
inference(forward_demodulation,[],[f14510,f107]) ).
fof(f107,plain,
! [X0] : multiply(sF1,multiply(b,X0)) = multiply(b,multiply(sF0,X0)),
inference(superposition,[],[f67,f66]) ).
fof(f14510,plain,
multiply(sF0,b) = multiply(sF0,multiply(sF1,multiply(b,sF0))),
inference(forward_demodulation,[],[f14509,f611]) ).
fof(f611,plain,
multiply(b,sF0) = multiply(sF1,multiply(a,sF0)),
inference(superposition,[],[f67,f576]) ).
fof(f576,plain,
sF0 = multiply(a,multiply(a,sF0)),
inference(superposition,[],[f71,f10]) ).
fof(f14509,plain,
multiply(sF0,b) = multiply(sF0,multiply(sF1,multiply(sF1,multiply(a,sF0)))),
inference(backward_demodulation,[],[f13645,f14508]) ).
fof(f14508,plain,
multiply(a,sF0) = multiply(sF0,multiply(sF0,b)),
inference(forward_demodulation,[],[f14507,f66]) ).
fof(f14507,plain,
multiply(a,sF0) = multiply(a,multiply(b,multiply(sF0,b))),
inference(forward_demodulation,[],[f14506,f13622]) ).
fof(f13622,plain,
multiply(b,multiply(sF0,b)) = multiply(sF1,multiply(sF1,sF0)),
inference(forward_demodulation,[],[f13599,f643]) ).
fof(f643,plain,
! [X2] : multiply(b,multiply(sF0,X2)) = multiply(sF1,multiply(a,multiply(sF0,X2))),
inference(forward_demodulation,[],[f642,f7]) ).
fof(f642,plain,
! [X2] : multiply(sF1,multiply(multiply(a,sF0),X2)) = multiply(b,multiply(sF0,X2)),
inference(forward_demodulation,[],[f632,f7]) ).
fof(f632,plain,
! [X2] : multiply(sF1,multiply(multiply(a,sF0),X2)) = multiply(multiply(b,sF0),X2),
inference(superposition,[],[f7,f611]) ).
fof(f13599,plain,
multiply(sF1,multiply(sF1,sF0)) = multiply(sF1,multiply(a,multiply(sF0,b))),
inference(superposition,[],[f115,f10893]) ).
fof(f10893,plain,
multiply(sF0,b) = multiply(a,multiply(sF1,sF0)),
inference(forward_demodulation,[],[f10892,f105]) ).
fof(f105,plain,
! [X0] : multiply(sF0,multiply(a,X0)) = multiply(a,multiply(sF1,X0)),
inference(forward_demodulation,[],[f104,f7]) ).
fof(f104,plain,
! [X0] : multiply(sF0,multiply(a,X0)) = multiply(multiply(a,sF1),X0),
inference(superposition,[],[f7,f96]) ).
fof(f96,plain,
multiply(sF0,a) = multiply(a,sF1),
inference(superposition,[],[f66,f11]) ).
fof(f10892,plain,
multiply(sF0,b) = multiply(sF0,multiply(a,sF0)),
inference(forward_demodulation,[],[f10891,f10800]) ).
fof(f10800,plain,
! [X10,X8] : multiply(X10,X8) = additive_inverse(multiply(X10,additive_inverse(X8))),
inference(forward_demodulation,[],[f10799,f260]) ).
fof(f260,plain,
! [X2,X0,X1] : additive_inverse(multiply(X0,X1)) = add(multiply(X0,X2),additive_inverse(multiply(X0,add(X1,X2)))),
inference(superposition,[],[f160,f3]) ).
fof(f10799,plain,
! [X10,X8,X9] : multiply(X10,X8) = add(multiply(X10,X9),additive_inverse(multiply(X10,add(additive_inverse(X8),X9)))),
inference(forward_demodulation,[],[f10544,f6]) ).
fof(f10544,plain,
! [X10,X8,X9] : multiply(X10,X8) = add(additive_inverse(multiply(X10,add(additive_inverse(X8),X9))),multiply(X10,X9)),
inference(superposition,[],[f5598,f38]) ).
fof(f5598,plain,
! [X82,X83,X84] : multiply(X82,X84) = add(additive_inverse(multiply(X82,X83)),multiply(X82,add(X84,X83))),
inference(forward_demodulation,[],[f5597,f6]) ).
fof(f5597,plain,
! [X82,X83,X84] : multiply(X82,X84) = add(multiply(X82,add(X84,X83)),additive_inverse(multiply(X82,X83))),
inference(forward_demodulation,[],[f5231,f1]) ).
fof(f5231,plain,
! [X82,X83,X84] : add(multiply(X82,add(X84,X83)),additive_inverse(multiply(X82,X83))) = add(multiply(X82,X84),additive_identity),
inference(superposition,[],[f261,f2]) ).
fof(f261,plain,
! [X3,X6,X4,X5] : add(multiply(X3,X4),add(multiply(X3,X5),X6)) = add(multiply(X3,add(X4,X5)),X6),
inference(superposition,[],[f5,f3]) ).
fof(f10891,plain,
multiply(sF0,b) = additive_inverse(multiply(sF0,additive_inverse(multiply(a,sF0)))),
inference(forward_demodulation,[],[f10608,f1]) ).
fof(f10608,plain,
multiply(sF0,b) = add(additive_inverse(multiply(sF0,additive_inverse(multiply(a,sF0)))),additive_identity),
inference(superposition,[],[f5598,f10209]) ).
fof(f10209,plain,
additive_identity = multiply(sF0,add(b,additive_inverse(multiply(a,sF0)))),
inference(forward_demodulation,[],[f10208,f2220]) ).
fof(f10208,plain,
multiply(sF0,additive_identity) = multiply(sF0,add(b,additive_inverse(multiply(a,sF0)))),
inference(forward_demodulation,[],[f10180,f8721]) ).
fof(f8721,plain,
! [X1] : additive_identity = multiply(add(b,additive_inverse(multiply(a,sF0))),multiply(sF0,X1)),
inference(superposition,[],[f7757,f577]) ).
fof(f577,plain,
! [X6] : multiply(sF0,X6) = multiply(a,multiply(a,multiply(sF0,X6))),
inference(superposition,[],[f71,f66]) ).
fof(f7757,plain,
! [X4] : additive_identity = multiply(add(b,additive_inverse(multiply(a,sF0))),multiply(a,X4)),
inference(forward_demodulation,[],[f7743,f7294]) ).
fof(f7743,plain,
! [X4] : multiply(additive_identity,X4) = multiply(add(b,additive_inverse(multiply(a,sF0))),multiply(a,X4)),
inference(superposition,[],[f7,f7711]) ).
fof(f7711,plain,
additive_identity = multiply(add(b,additive_inverse(multiply(a,sF0))),a),
inference(forward_demodulation,[],[f7710,f2220]) ).
fof(f7710,plain,
multiply(add(b,additive_inverse(multiply(a,sF0))),additive_identity) = multiply(add(b,additive_inverse(multiply(a,sF0))),a),
inference(forward_demodulation,[],[f7670,f7307]) ).
fof(f7307,plain,
! [X4] : additive_identity = multiply(a,multiply(add(b,additive_inverse(multiply(a,sF0))),X4)),
inference(backward_demodulation,[],[f6067,f7294]) ).
fof(f6067,plain,
! [X4] : multiply(additive_identity,X4) = multiply(a,multiply(add(b,additive_inverse(multiply(a,sF0))),X4)),
inference(superposition,[],[f7,f6022]) ).
fof(f6022,plain,
additive_identity = multiply(a,add(b,additive_inverse(multiply(a,sF0)))),
inference(forward_demodulation,[],[f5983,f2220]) ).
fof(f5983,plain,
multiply(a,additive_identity) = multiply(a,add(b,additive_inverse(multiply(a,sF0)))),
inference(superposition,[],[f618,f2]) ).
fof(f618,plain,
! [X1] : multiply(a,add(multiply(a,sF0),X1)) = multiply(a,add(b,X1)),
inference(forward_demodulation,[],[f614,f240]) ).
fof(f240,plain,
! [X6] : multiply(a,add(b,X6)) = add(sF0,multiply(a,X6)),
inference(superposition,[],[f3,f10]) ).
fof(f614,plain,
! [X1] : multiply(a,add(multiply(a,sF0),X1)) = add(sF0,multiply(a,X1)),
inference(superposition,[],[f3,f576]) ).
fof(f7670,plain,
multiply(add(b,additive_inverse(multiply(a,sF0))),multiply(a,multiply(add(b,additive_inverse(multiply(a,sF0))),additive_identity))) = multiply(add(b,additive_inverse(multiply(a,sF0))),a),
inference(superposition,[],[f74,f7307]) ).
fof(f10180,plain,
multiply(sF0,multiply(add(b,additive_inverse(multiply(a,sF0))),multiply(sF0,additive_identity))) = multiply(sF0,add(b,additive_inverse(multiply(a,sF0)))),
inference(superposition,[],[f74,f8721]) ).
fof(f115,plain,
! [X0] : multiply(sF1,X0) = multiply(sF1,multiply(a,multiply(a,X0))),
inference(forward_demodulation,[],[f114,f7]) ).
fof(f114,plain,
! [X0] : multiply(sF1,X0) = multiply(sF1,multiply(multiply(a,a),X0)),
inference(superposition,[],[f7,f111]) ).
fof(f111,plain,
sF1 = multiply(sF1,multiply(a,a)),
inference(forward_demodulation,[],[f108,f11]) ).
fof(f108,plain,
multiply(b,a) = multiply(sF1,multiply(a,a)),
inference(superposition,[],[f67,f8]) ).
fof(f14506,plain,
multiply(a,sF0) = multiply(a,multiply(sF1,multiply(sF1,sF0))),
inference(forward_demodulation,[],[f14505,f105]) ).
fof(f14505,plain,
multiply(a,sF0) = multiply(sF0,multiply(a,multiply(sF1,sF0))),
inference(forward_demodulation,[],[f14480,f105]) ).
fof(f14480,plain,
multiply(a,sF0) = multiply(sF0,multiply(sF0,multiply(a,sF0))),
inference(superposition,[],[f71,f14424]) ).
fof(f13645,plain,
multiply(sF0,b) = multiply(sF0,multiply(sF1,multiply(sF1,multiply(sF0,multiply(sF0,b))))),
inference(forward_demodulation,[],[f13644,f7]) ).
fof(f13644,plain,
multiply(sF0,b) = multiply(sF0,multiply(sF1,multiply(multiply(sF1,sF0),multiply(sF0,b)))),
inference(forward_demodulation,[],[f13643,f67]) ).
fof(f13643,plain,
multiply(sF0,b) = multiply(sF0,multiply(b,multiply(a,multiply(multiply(sF1,sF0),multiply(sF0,b))))),
inference(forward_demodulation,[],[f13642,f13635]) ).
fof(f13635,plain,
! [X6] : multiply(sF0,multiply(b,X6)) = multiply(a,multiply(sF1,multiply(sF0,X6))),
inference(forward_demodulation,[],[f13634,f7]) ).
fof(f13634,plain,
! [X6] : multiply(multiply(sF0,b),X6) = multiply(a,multiply(sF1,multiply(sF0,X6))),
inference(forward_demodulation,[],[f13608,f7]) ).
fof(f13608,plain,
! [X6] : multiply(multiply(sF0,b),X6) = multiply(a,multiply(multiply(sF1,sF0),X6)),
inference(superposition,[],[f7,f10893]) ).
fof(f13642,plain,
multiply(sF0,b) = multiply(a,multiply(sF1,multiply(sF0,multiply(a,multiply(multiply(sF1,sF0),multiply(sF0,b)))))),
inference(forward_demodulation,[],[f13610,f7]) ).
fof(f13610,plain,
multiply(sF0,b) = multiply(a,multiply(multiply(sF1,sF0),multiply(a,multiply(multiply(sF1,sF0),multiply(sF0,b))))),
inference(superposition,[],[f74,f10893]) ).
fof(f676,plain,
! [X8,X6,X7,X5] : multiply(add(X8,multiply(X5,X6)),X7) = add(multiply(X8,X7),multiply(X5,multiply(X6,X7))),
inference(superposition,[],[f4,f7]) ).
fof(f13304,plain,
additive_identity = multiply(add(additive_inverse(b),multiply(a,sF0)),sF0),
inference(backward_demodulation,[],[f11250,f13297]) ).
fof(f11250,plain,
additive_identity = multiply(add(b,multiply(a,additive_inverse(sF0))),additive_inverse(sF0)),
inference(backward_demodulation,[],[f8720,f11060]) ).
fof(f8720,plain,
additive_identity = multiply(add(b,additive_inverse(multiply(a,sF0))),additive_inverse(sF0)),
inference(superposition,[],[f7757,f2469]) ).
fof(f2469,plain,
additive_inverse(sF0) = multiply(a,multiply(a,additive_inverse(sF0))),
inference(superposition,[],[f577,f2414]) ).
fof(f16057,plain,
multiply(b,multiply(add(sF0,additive_inverse(sF1)),multiply(b,additive_identity))) = multiply(b,add(sF0,additive_inverse(sF1))),
inference(superposition,[],[f74,f15214]) ).
fof(f11060,plain,
! [X14,X13] : multiply(X14,additive_inverse(X13)) = additive_inverse(multiply(X14,X13)),
inference(superposition,[],[f10800,f55]) ).
fof(f14566,plain,
add(sF1,additive_inverse(sF0)) = multiply(b,multiply(b,add(sF1,additive_inverse(sF0)))),
inference(forward_demodulation,[],[f14565,f1197]) ).
fof(f1197,plain,
! [X50,X48,X49,X47] : multiply(X50,multiply(X47,add(X48,X49))) = multiply(X50,multiply(X47,add(X49,X48))),
inference(forward_demodulation,[],[f1155,f3]) ).
fof(f1155,plain,
! [X50,X48,X49,X47] : multiply(X50,add(multiply(X47,X49),multiply(X47,X48))) = multiply(X50,multiply(X47,add(X48,X49))),
inference(superposition,[],[f289,f3]) ).
fof(f289,plain,
! [X3,X4,X5] : multiply(X3,add(X4,X5)) = multiply(X3,add(X5,X4)),
inference(forward_demodulation,[],[f258,f3]) ).
fof(f258,plain,
! [X3,X4,X5] : add(multiply(X3,X5),multiply(X3,X4)) = multiply(X3,add(X4,X5)),
inference(superposition,[],[f3,f6]) ).
fof(f14565,plain,
add(sF1,additive_inverse(sF0)) = multiply(b,multiply(b,add(additive_inverse(sF0),sF1))),
inference(forward_demodulation,[],[f14543,f6124]) ).
fof(f6124,plain,
! [X4] : multiply(b,add(a,multiply(b,X4))) = multiply(b,multiply(b,add(X4,sF1))),
inference(superposition,[],[f626,f3]) ).
fof(f626,plain,
! [X0] : multiply(b,add(a,X0)) = multiply(b,add(X0,multiply(b,sF1))),
inference(forward_demodulation,[],[f625,f242]) ).
fof(f625,plain,
! [X0] : add(sF1,multiply(b,X0)) = multiply(b,add(X0,multiply(b,sF1))),
inference(forward_demodulation,[],[f622,f6]) ).
fof(f622,plain,
! [X0] : multiply(b,add(X0,multiply(b,sF1))) = add(multiply(b,X0),sF1),
inference(superposition,[],[f3,f578]) ).
fof(f14543,plain,
multiply(b,add(a,multiply(b,additive_inverse(sF0)))) = add(sF1,additive_inverse(sF0)),
inference(superposition,[],[f242,f14469]) ).
fof(f14469,plain,
additive_inverse(sF0) = multiply(b,multiply(b,additive_inverse(sF0))),
inference(forward_demodulation,[],[f14442,f11060]) ).
fof(f14442,plain,
additive_inverse(sF0) = multiply(b,additive_inverse(multiply(b,sF0))),
inference(superposition,[],[f11060,f14391]) ).
fof(f44,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[],[f38,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 02:25:34 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.36 This is a CNF_UNS_RFO_PEQ_UEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.l6WI4Y6Rsm/Vampire---4.8_5115
% 0.15/0.36 % (5230)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (5237)lrs+10_10_av=off:drc=off:sp=frequency:tgt=ground:stl=62_102 on Vampire---4 for (102ds/0Mi)
% 0.21/0.42 % (5232)lrs+10_5_av=off:drc=off:fde=none:nwc=1.1:sp=scramble:to=lpo:tgt=ground:stl=62_518 on Vampire---4 for (518ds/0Mi)
% 0.21/0.42 % (5231)lrs+10_4:3_av=off:bd=preordered:drc=off:fde=unused:nwc=1.7:sp=weighted_frequency:to=lpo:tgt=ground:stl=125_692 on Vampire---4 for (692ds/0Mi)
% 0.21/0.42 % (5233)lrs+10_16_av=off:drc=off:nwc=1.5:sp=scramble:tgt=ground:stl=125_501 on Vampire---4 for (501ds/0Mi)
% 0.21/0.42 % (5234)lrs+10_20_av=off:bd=preordered:drc=off:fde=unused:sims=off:to=lpo:stl=62_369 on Vampire---4 for (369ds/0Mi)
% 0.21/0.42 % (5236)dis+10_50_av=off:bd=preordered:drc=off:fde=unused:nwc=1.5:sims=off:sp=reverse_weighted_frequency:to=lpo_239 on Vampire---4 for (239ds/0Mi)
% 0.21/0.42 % (5235)lrs+10_64_av=off:bd=off:drc=off:fde=unused:sp=frequency:tgt=full:stl=62_243 on Vampire---4 for (243ds/0Mi)
% 3.52/0.89 % (5237)First to succeed.
% 3.52/0.90 % (5237)Refutation found. Thanks to Tanya!
% 3.52/0.90 % SZS status Unsatisfiable for Vampire---4
% 3.52/0.90 % SZS output start Proof for Vampire---4
% See solution above
% 3.52/0.90 % (5237)------------------------------
% 3.52/0.90 % (5237)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 3.52/0.90 % (5237)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 3.52/0.90 % (5237)Termination reason: Refutation
% 3.52/0.90
% 3.52/0.90 % (5237)Memory used [KB]: 19317
% 3.52/0.90 % (5237)Time elapsed: 0.496 s
% 3.52/0.90 % (5237)------------------------------
% 3.52/0.90 % (5237)------------------------------
% 3.52/0.90 % (5230)Success in time 0.524 s
% 3.52/0.90 % Vampire---4.8 exiting
%------------------------------------------------------------------------------