TSTP Solution File: BOO008-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO008-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 May 20 18:58:45 EDT 2024
% Result : Unsatisfiable 52.68s 7.90s
% Output : Refutation 52.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 15
% Syntax : Number of formulae : 198 ( 198 unt; 0 def)
% Number of atoms : 198 ( 197 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 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 : 370 ( 370 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f382931,plain,
$false,
inference(trivial_inequality_removal,[],[f382489]) ).
fof(f382489,plain,
add(a,add(b,c)) != add(a,add(b,c)),
inference(superposition,[],[f15,f322186]) ).
fof(f322186,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(forward_demodulation,[],[f322185,f17308]) ).
fof(f17308,plain,
! [X0,X1] : add(X1,X0) = add(multiply(inverse(X1),X0),X1),
inference(superposition,[],[f12119,f2]) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f12119,plain,
! [X0,X1] : add(X0,X1) = add(multiply(X1,inverse(X0)),X0),
inference(forward_demodulation,[],[f12118,f4869]) ).
fof(f4869,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(X0,X1)),
inference(superposition,[],[f2798,f1]) ).
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2798,plain,
! [X0,X1] : add(X0,X1) = add(add(X0,X1),X0),
inference(superposition,[],[f2159,f2497]) ).
fof(f2497,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(superposition,[],[f2166,f2]) ).
fof(f2166,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f2165,f13]) ).
fof(f13,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
fof(f2165,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(add(X0,X1),X0),
inference(forward_demodulation,[],[f2005,f1945]) ).
fof(f1945,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[],[f1918,f23]) ).
fof(f23,plain,
additive_identity = inverse(multiplicative_identity),
inference(superposition,[],[f9,f12]) ).
fof(f12,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f1918,plain,
! [X0] : inverse(multiplicative_identity) = multiply(X0,additive_identity),
inference(superposition,[],[f663,f1873]) ).
fof(f1873,plain,
! [X0] : multiplicative_identity = inverse(multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f1872,f7]) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f1872,plain,
! [X0] : inverse(multiply(X0,additive_identity)) = add(multiply(X0,additive_identity),inverse(multiply(X0,additive_identity))),
inference(forward_demodulation,[],[f1852,f12]) ).
fof(f1852,plain,
! [X0] : add(multiply(X0,additive_identity),inverse(multiply(X0,additive_identity))) = multiply(multiplicative_identity,inverse(multiply(X0,additive_identity))),
inference(superposition,[],[f68,f1836]) ).
fof(f1836,plain,
! [X0] : multiplicative_identity = add(X0,inverse(multiply(X0,additive_identity))),
inference(forward_demodulation,[],[f1826,f7]) ).
fof(f1826,plain,
! [X0] : add(X0,inverse(multiply(X0,additive_identity))) = add(multiply(X0,additive_identity),inverse(multiply(X0,additive_identity))),
inference(superposition,[],[f78,f1508]) ).
fof(f1508,plain,
! [X0] : multiply(X0,additive_identity) = multiply(X0,multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f1507,f594]) ).
fof(f594,plain,
! [X0] : multiply(X0,additive_identity) = multiply(multiply(X0,X0),multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f559,f95]) ).
fof(f95,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f82,f14]) ).
fof(f14,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
fof(f82,plain,
! [X0] : add(additive_identity,X0) = add(X0,X0),
inference(superposition,[],[f76,f10]) ).
fof(f10,axiom,
! [X0] : additive_identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f76,plain,
! [X0,X1] : add(X1,X0) = add(multiply(inverse(X0),X1),X0),
inference(forward_demodulation,[],[f63,f12]) ).
fof(f63,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = multiply(multiplicative_identity,add(X1,X0)),
inference(superposition,[],[f3,f8]) ).
fof(f8,axiom,
! [X0] : multiplicative_identity = add(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f559,plain,
! [X0] : multiply(multiply(X0,X0),multiply(X0,additive_identity)) = add(multiply(X0,additive_identity),multiply(X0,additive_identity)),
inference(superposition,[],[f68,f378]) ).
fof(f378,plain,
! [X0] : multiply(X0,X0) = add(X0,multiply(X0,additive_identity)),
inference(superposition,[],[f321,f1]) ).
fof(f321,plain,
! [X0] : multiply(X0,X0) = add(multiply(X0,additive_identity),X0),
inference(superposition,[],[f258,f2]) ).
fof(f258,plain,
! [X0] : add(multiply(additive_identity,X0),X0) = multiply(X0,X0),
inference(superposition,[],[f62,f95]) ).
fof(f62,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = multiply(X0,add(X1,X0)),
inference(superposition,[],[f3,f14]) ).
fof(f1507,plain,
! [X0] : multiply(multiply(X0,X0),multiply(X0,additive_identity)) = multiply(X0,multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f1506,f14]) ).
fof(f1506,plain,
! [X0] : multiply(multiply(X0,X0),multiply(X0,additive_identity)) = multiply(X0,add(additive_identity,multiply(X0,additive_identity))),
inference(forward_demodulation,[],[f1451,f6]) ).
fof(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f1451,plain,
! [X0] : multiply(multiply(X0,X0),multiply(X0,additive_identity)) = add(multiply(X0,additive_identity),multiply(X0,multiply(X0,additive_identity))),
inference(superposition,[],[f106,f378]) ).
fof(f106,plain,
! [X0,X1] : multiply(add(X1,X0),X0) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f104,f1]) ).
fof(f104,plain,
! [X0,X1] : multiply(add(X1,X0),X0) = add(multiply(X1,X0),X0),
inference(superposition,[],[f3,f95]) ).
fof(f78,plain,
! [X0,X1] : add(X1,inverse(X0)) = add(multiply(X1,X0),inverse(X0)),
inference(forward_demodulation,[],[f65,f11]) ).
fof(f11,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f65,plain,
! [X0,X1] : add(multiply(X1,X0),inverse(X0)) = multiply(add(X1,inverse(X0)),multiplicative_identity),
inference(superposition,[],[f3,f7]) ).
fof(f68,plain,
! [X0,X1] : add(multiply(X1,additive_identity),X0) = multiply(add(X1,X0),X0),
inference(superposition,[],[f3,f14]) ).
fof(f663,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f662,f130]) ).
fof(f130,plain,
! [X0] : add(X0,inverse(inverse(X0))) = X0,
inference(superposition,[],[f97,f1]) ).
fof(f97,plain,
! [X0] : add(inverse(inverse(X0)),X0) = X0,
inference(forward_demodulation,[],[f84,f14]) ).
fof(f84,plain,
! [X0] : add(additive_identity,X0) = add(inverse(inverse(X0)),X0),
inference(superposition,[],[f76,f9]) ).
fof(f662,plain,
! [X0] : inverse(inverse(X0)) = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[],[f638,f14]) ).
fof(f638,plain,
! [X0] : add(X0,inverse(inverse(X0))) = add(additive_identity,inverse(inverse(X0))),
inference(superposition,[],[f75,f10]) ).
fof(f75,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(X0)) = add(X1,inverse(X0)),
inference(forward_demodulation,[],[f59,f12]) ).
fof(f59,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[],[f3,f7]) ).
fof(f2005,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(add(X0,X1),X0),
inference(superposition,[],[f4,f13]) ).
fof(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f2159,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(forward_demodulation,[],[f2158,f2142]) ).
fof(f2142,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = X0,
inference(forward_demodulation,[],[f2141,f13]) ).
fof(f2141,plain,
! [X0,X1] : add(X0,additive_identity) = add(multiply(additive_identity,X1),X0),
inference(forward_demodulation,[],[f2140,f1945]) ).
fof(f2140,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = add(X0,multiply(X1,additive_identity)),
inference(forward_demodulation,[],[f2139,f1945]) ).
fof(f2139,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = add(X0,multiply(X1,multiply(X0,additive_identity))),
inference(forward_demodulation,[],[f2138,f259]) ).
fof(f259,plain,
! [X0,X1] : add(multiply(additive_identity,X0),X1) = multiply(X1,add(X1,X0)),
inference(superposition,[],[f62,f1]) ).
fof(f2138,plain,
! [X0,X1] : add(X0,multiply(X1,multiply(X0,additive_identity))) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[],[f2137,f2]) ).
fof(f2137,plain,
! [X0,X1] : add(X0,multiply(X1,multiply(X0,additive_identity))) = multiply(add(X0,X1),X0),
inference(forward_demodulation,[],[f1993,f1733]) ).
fof(f1733,plain,
! [X0] : multiply(X0,X0) = X0,
inference(forward_demodulation,[],[f1708,f14]) ).
fof(f1708,plain,
! [X0] : add(additive_identity,X0) = multiply(X0,X0),
inference(superposition,[],[f273,f1707]) ).
fof(f1707,plain,
additive_identity = multiply(additive_identity,additive_identity),
inference(forward_demodulation,[],[f1683,f23]) ).
fof(f1683,plain,
inverse(multiplicative_identity) = multiply(additive_identity,additive_identity),
inference(superposition,[],[f663,f1637]) ).
fof(f1637,plain,
multiplicative_identity = inverse(multiply(additive_identity,additive_identity)),
inference(superposition,[],[f1628,f14]) ).
fof(f1628,plain,
! [X0] : multiplicative_identity = add(X0,inverse(multiply(X0,X0))),
inference(forward_demodulation,[],[f1619,f8]) ).
fof(f1619,plain,
! [X0] : add(X0,inverse(multiply(X0,X0))) = add(inverse(multiply(X0,X0)),multiply(X0,X0)),
inference(superposition,[],[f644,f1536]) ).
fof(f1536,plain,
! [X0] : multiply(X0,X0) = multiply(multiply(X0,X0),X0),
inference(forward_demodulation,[],[f1535,f378]) ).
fof(f1535,plain,
! [X0] : multiply(multiply(X0,X0),X0) = add(X0,multiply(X0,additive_identity)),
inference(forward_demodulation,[],[f1534,f1508]) ).
fof(f1534,plain,
! [X0] : multiply(multiply(X0,X0),X0) = add(X0,multiply(X0,multiply(X0,additive_identity))),
inference(forward_demodulation,[],[f1469,f2]) ).
fof(f1469,plain,
! [X0] : multiply(multiply(X0,X0),X0) = add(X0,multiply(multiply(X0,additive_identity),X0)),
inference(superposition,[],[f106,f321]) ).
fof(f644,plain,
! [X0,X1] : add(X1,inverse(X0)) = add(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f75,f1]) ).
fof(f273,plain,
! [X0] : multiply(X0,X0) = add(multiply(additive_identity,additive_identity),X0),
inference(superposition,[],[f62,f14]) ).
fof(f1993,plain,
! [X0,X1] : add(X0,multiply(X1,multiply(X0,additive_identity))) = multiply(add(X0,X1),multiply(X0,X0)),
inference(superposition,[],[f4,f378]) ).
fof(f2158,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f2157,f663]) ).
fof(f2157,plain,
! [X0,X1] : add(multiply(additive_identity,X1),X0) = add(X0,multiply(X1,inverse(inverse(X0)))),
inference(forward_demodulation,[],[f2156,f259]) ).
fof(f2156,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(inverse(X0)))) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[],[f2001,f2]) ).
fof(f2001,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(inverse(X0)))) = multiply(add(X0,X1),X0),
inference(superposition,[],[f4,f130]) ).
fof(f12118,plain,
! [X0,X1] : add(multiply(X1,inverse(X0)),X0) = add(X0,add(X0,X1)),
inference(forward_demodulation,[],[f12117,f1]) ).
fof(f12117,plain,
! [X0,X1] : add(multiply(X1,inverse(X0)),X0) = add(add(X0,X1),X0),
inference(forward_demodulation,[],[f11997,f663]) ).
fof(f11997,plain,
! [X0,X1] : add(multiply(X1,inverse(X0)),X0) = add(add(inverse(inverse(X0)),X1),X0),
inference(superposition,[],[f79,f9508]) ).
fof(f9508,plain,
! [X0,X1] : multiply(X1,X0) = multiply(add(inverse(X0),X1),X0),
inference(forward_demodulation,[],[f9358,f14]) ).
fof(f9358,plain,
! [X0,X1] : add(additive_identity,multiply(X1,X0)) = multiply(add(inverse(X0),X1),X0),
inference(superposition,[],[f5,f10]) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f79,plain,
! [X0,X1] : add(X1,X0) = add(multiply(X1,inverse(X0)),X0),
inference(forward_demodulation,[],[f69,f11]) ).
fof(f69,plain,
! [X0,X1] : add(multiply(X1,inverse(X0)),X0) = multiply(add(X1,X0),multiplicative_identity),
inference(superposition,[],[f3,f8]) ).
fof(f322185,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(multiply(inverse(X0),add(X1,X2)),X0),
inference(forward_demodulation,[],[f322184,f63616]) ).
fof(f63616,plain,
! [X2,X0,X1] : multiply(inverse(X0),add(add(X0,X1),X2)) = multiply(inverse(X0),add(X1,X2)),
inference(forward_demodulation,[],[f63342,f6]) ).
fof(f63342,plain,
! [X2,X0,X1] : multiply(inverse(X0),add(add(X0,X1),X2)) = add(multiply(inverse(X0),X1),multiply(inverse(X0),X2)),
inference(superposition,[],[f6,f27370]) ).
fof(f27370,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(inverse(X0),add(X0,X1)),
inference(forward_demodulation,[],[f27112,f14]) ).
fof(f27112,plain,
! [X0,X1] : multiply(inverse(X0),add(X0,X1)) = add(additive_identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f6,f10]) ).
fof(f322184,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(multiply(inverse(X0),add(add(X0,X1),X2)),X0),
inference(forward_demodulation,[],[f321366,f2]) ).
fof(f321366,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(multiply(add(add(X0,X1),X2),inverse(X0)),X0),
inference(superposition,[],[f317476,f9498]) ).
fof(f9498,plain,
! [X2,X0,X1] : multiply(add(add(X0,X1),X2),X0) = X0,
inference(forward_demodulation,[],[f9350,f2159]) ).
fof(f9350,plain,
! [X2,X0,X1] : add(X0,multiply(X2,X0)) = multiply(add(add(X0,X1),X2),X0),
inference(superposition,[],[f5,f2166]) ).
fof(f317476,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f316998,f663]) ).
fof(f316998,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),inverse(inverse(multiply(X0,X1)))) = X0,
inference(superposition,[],[f64004,f316137]) ).
fof(f316137,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = add(inverse(X0),inverse(X1)),
inference(forward_demodulation,[],[f316136,f2871]) ).
fof(f2871,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f2870,f2142]) ).
fof(f2870,plain,
! [X0,X1] : add(multiply(additive_identity,X0),multiply(X1,X0)) = multiply(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f2837,f2]) ).
fof(f2837,plain,
! [X0,X1] : add(multiply(additive_identity,X0),multiply(X1,X0)) = multiply(multiply(X1,X0),X0),
inference(superposition,[],[f62,f2159]) ).
fof(f316136,plain,
! [X0,X1] : add(inverse(X0),inverse(X1)) = inverse(multiply(X1,multiply(X0,X1))),
inference(forward_demodulation,[],[f316135,f663]) ).
fof(f316135,plain,
! [X0,X1] : add(inverse(X0),inverse(X1)) = inverse(multiply(inverse(inverse(X1)),multiply(X0,X1))),
inference(forward_demodulation,[],[f316134,f315772]) ).
fof(f315772,plain,
! [X0,X1] : add(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f315771,f16465]) ).
fof(f16465,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,add(X0,inverse(X1))),
inference(superposition,[],[f9567,f2]) ).
fof(f9567,plain,
! [X0,X1] : multiply(X1,X0) = multiply(add(X1,inverse(X0)),X0),
inference(forward_demodulation,[],[f9396,f13]) ).
fof(f9396,plain,
! [X0,X1] : add(multiply(X1,X0),additive_identity) = multiply(add(X1,inverse(X0)),X0),
inference(superposition,[],[f5,f10]) ).
fof(f315771,plain,
! [X0,X1] : add(inverse(X0),X1) = inverse(multiply(X0,add(inverse(X1),inverse(X0)))),
inference(forward_demodulation,[],[f315770,f663]) ).
fof(f315770,plain,
! [X0,X1] : add(inverse(X0),X1) = inverse(multiply(X0,inverse(inverse(add(inverse(X1),inverse(X0)))))),
inference(forward_demodulation,[],[f315769,f117786]) ).
fof(f117786,plain,
! [X0,X1] : inverse(add(inverse(X0),X1)) = multiply(X0,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f117069,f63521]) ).
fof(f63521,plain,
! [X2,X0,X1] : inverse(add(X0,X1)) = multiply(inverse(add(X0,X1)),inverse(multiply(X2,X1))),
inference(forward_demodulation,[],[f63262,f11]) ).
fof(f63262,plain,
! [X2,X0,X1] : multiply(inverse(add(X0,X1)),multiplicative_identity) = multiply(inverse(add(X0,X1)),inverse(multiply(X2,X1))),
inference(superposition,[],[f27370,f7397]) ).
fof(f7397,plain,
! [X2,X0,X1] : multiplicative_identity = add(add(X1,X0),inverse(multiply(X2,X0))),
inference(superposition,[],[f5411,f2588]) ).
fof(f2588,plain,
! [X0,X1] : multiply(X1,add(X0,X1)) = X1,
inference(superposition,[],[f2452,f2]) ).
fof(f2452,plain,
! [X0,X1] : multiply(add(X1,X0),X0) = X0,
inference(superposition,[],[f2166,f1]) ).
fof(f5411,plain,
! [X2,X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X1,multiply(X2,X0)))),
inference(superposition,[],[f2624,f2869]) ).
fof(f2869,plain,
! [X2,X0,X1] : add(X0,multiply(X2,multiply(X1,X0))) = X0,
inference(forward_demodulation,[],[f2868,f2142]) ).
fof(f2868,plain,
! [X2,X0,X1] : add(X0,multiply(X2,multiply(X1,X0))) = add(multiply(additive_identity,X2),X0),
inference(forward_demodulation,[],[f2867,f259]) ).
fof(f2867,plain,
! [X2,X0,X1] : multiply(X0,add(X0,X2)) = add(X0,multiply(X2,multiply(X1,X0))),
inference(forward_demodulation,[],[f2836,f2]) ).
fof(f2836,plain,
! [X2,X0,X1] : add(X0,multiply(X2,multiply(X1,X0))) = multiply(add(X0,X2),X0),
inference(superposition,[],[f4,f2159]) ).
fof(f2624,plain,
! [X0,X1] : multiplicative_identity = add(add(X0,X1),inverse(X1)),
inference(forward_demodulation,[],[f2596,f7]) ).
fof(f2596,plain,
! [X0,X1] : add(add(X0,X1),inverse(X1)) = add(X1,inverse(X1)),
inference(superposition,[],[f78,f2452]) ).
fof(f117069,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X0,X1))) = multiply(inverse(add(inverse(X0),X1)),inverse(multiply(X0,X1))),
inference(superposition,[],[f9489,f64004]) ).
fof(f9489,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = multiply(add(X0,X1),inverse(X0)),
inference(forward_demodulation,[],[f9342,f14]) ).
fof(f9342,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(superposition,[],[f5,f9]) ).
fof(f315769,plain,
! [X0,X1] : add(inverse(X0),X1) = inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X1,inverse(X0))))))),
inference(forward_demodulation,[],[f315768,f2]) ).
fof(f315768,plain,
! [X0,X1] : add(inverse(X0),X1) = inverse(multiply(inverse(multiply(X1,inverse(multiply(X1,inverse(X0))))),X0)),
inference(forward_demodulation,[],[f315014,f4081]) ).
fof(f4081,plain,
! [X2,X0,X1] : add(X0,X2) = add(X0,multiply(X2,inverse(multiply(X1,X0)))),
inference(forward_demodulation,[],[f4040,f11]) ).
fof(f4040,plain,
! [X2,X0,X1] : multiply(add(X0,X2),multiplicative_identity) = add(X0,multiply(X2,inverse(multiply(X1,X0)))),
inference(superposition,[],[f4,f3463]) ).
fof(f3463,plain,
! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f2624,f2159]) ).
fof(f315014,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X1,inverse(multiply(X1,inverse(X0))))),X0)) = add(inverse(X0),multiply(X1,inverse(multiply(X1,inverse(X0))))),
inference(superposition,[],[f67921,f108635]) ).
fof(f108635,plain,
! [X0,X1] : add(X1,multiply(X0,inverse(multiply(X0,inverse(X1))))) = X1,
inference(forward_demodulation,[],[f108634,f2497]) ).
fof(f108634,plain,
! [X0,X1] : add(X1,multiply(X0,inverse(multiply(X0,inverse(X1))))) = multiply(X1,add(X1,multiply(X0,inverse(multiply(X0,inverse(X1)))))),
inference(forward_demodulation,[],[f108633,f15421]) ).
fof(f15421,plain,
! [X2,X0,X1] : multiply(add(X2,X0),inverse(multiply(X1,inverse(X0)))) = add(X0,multiply(X2,inverse(multiply(X1,inverse(X0))))),
inference(forward_demodulation,[],[f15309,f1]) ).
fof(f15309,plain,
! [X2,X0,X1] : multiply(add(X2,X0),inverse(multiply(X1,inverse(X0)))) = add(multiply(X2,inverse(multiply(X1,inverse(X0)))),X0),
inference(superposition,[],[f5,f14958]) ).
fof(f14958,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,inverse(X1)))) = X1,
inference(superposition,[],[f12089,f2]) ).
fof(f12089,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(X0))),X0) = X0,
inference(forward_demodulation,[],[f11922,f12]) ).
fof(f11922,plain,
! [X0,X1] : multiply(multiplicative_identity,X0) = multiply(inverse(multiply(X1,inverse(X0))),X0),
inference(superposition,[],[f9508,f3463]) ).
fof(f108633,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(multiply(X0,inverse(X1)))) = multiply(X1,multiply(add(X0,X1),inverse(multiply(X0,inverse(X1))))),
inference(forward_demodulation,[],[f108159,f2]) ).
fof(f108159,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),add(X0,X1)) = multiply(X1,multiply(inverse(multiply(X0,inverse(X1))),add(X0,X1))),
inference(superposition,[],[f14665,f61643]) ).
fof(f61643,plain,
! [X0,X1] : multiply(add(X0,X1),inverse(multiply(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[],[f61378,f14958]) ).
fof(f61378,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,inverse(X1)))) = multiply(add(X0,X1),inverse(multiply(X0,inverse(X1)))),
inference(superposition,[],[f9489,f79]) ).
fof(f14665,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X1,X0),multiply(X0,X1)),
inference(forward_demodulation,[],[f14533,f3054]) ).
fof(f3054,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f3053,f2142]) ).
fof(f3053,plain,
! [X0,X1] : add(multiply(additive_identity,X0),multiply(X0,X1)) = multiply(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f3023,f2]) ).
fof(f3023,plain,
! [X0,X1] : add(multiply(additive_identity,X0),multiply(X0,X1)) = multiply(multiply(X0,X1),X0),
inference(superposition,[],[f62,f2793]) ).
fof(f2793,plain,
! [X0,X1] : add(X1,multiply(X1,X0)) = X1,
inference(superposition,[],[f2159,f2]) ).
fof(f14533,plain,
! [X0,X1] : multiply(X0,multiply(X0,X1)) = multiply(multiply(X1,X0),multiply(X0,X1)),
inference(superposition,[],[f12030,f12030]) ).
fof(f12030,plain,
! [X0,X1] : multiply(X1,X0) = multiply(multiply(X0,X1),X0),
inference(forward_demodulation,[],[f11894,f9567]) ).
fof(f11894,plain,
! [X0,X1] : multiply(multiply(X0,X1),X0) = multiply(add(X1,inverse(X0)),X0),
inference(superposition,[],[f9508,f644]) ).
fof(f67921,plain,
! [X0,X1] : add(inverse(add(X0,X1)),X1) = inverse(multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f67332,f66172]) ).
fof(f66172,plain,
! [X2,X0,X1] : inverse(multiply(X2,X0)) = add(inverse(multiply(X2,X0)),inverse(add(X0,X1))),
inference(forward_demodulation,[],[f65886,f14]) ).
fof(f65886,plain,
! [X2,X0,X1] : add(additive_identity,inverse(multiply(X2,X0))) = add(inverse(multiply(X2,X0)),inverse(add(X0,X1))),
inference(superposition,[],[f12111,f34323]) ).
fof(f34323,plain,
! [X2,X0,X1] : additive_identity = multiply(inverse(add(X1,X2)),multiply(X0,X1)),
inference(superposition,[],[f13649,f5053]) ).
fof(f5053,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = X0,
inference(superposition,[],[f2866,f191]) ).
fof(f191,plain,
! [X0,X1] : add(X0,X1) = add(X1,multiply(X0,inverse(X1))),
inference(superposition,[],[f79,f1]) ).
fof(f2866,plain,
! [X2,X0,X1] : add(X0,multiply(multiply(X1,X0),X2)) = X0,
inference(forward_demodulation,[],[f2865,f2142]) ).
fof(f2865,plain,
! [X2,X0,X1] : add(X0,multiply(multiply(X1,X0),X2)) = add(multiply(additive_identity,X2),X0),
inference(forward_demodulation,[],[f2835,f259]) ).
fof(f2835,plain,
! [X2,X0,X1] : add(X0,multiply(multiply(X1,X0),X2)) = multiply(X0,add(X0,X2)),
inference(superposition,[],[f4,f2159]) ).
fof(f13649,plain,
! [X2,X0,X1] : additive_identity = multiply(inverse(add(add(X0,X1),X2)),X0),
inference(superposition,[],[f12510,f9771]) ).
fof(f9771,plain,
! [X2,X0,X1] : multiply(X0,add(add(X0,X1),X2)) = X0,
inference(superposition,[],[f9498,f2]) ).
fof(f12510,plain,
! [X0,X1] : additive_identity = multiply(inverse(X1),multiply(X0,X1)),
inference(superposition,[],[f12132,f2]) ).
fof(f12132,plain,
! [X0,X1] : additive_identity = multiply(multiply(X1,X0),inverse(X0)),
inference(superposition,[],[f12053,f663]) ).
fof(f12053,plain,
! [X0,X1] : additive_identity = multiply(multiply(X1,inverse(X0)),X0),
inference(forward_demodulation,[],[f12052,f9]) ).
fof(f12052,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(multiply(X1,inverse(X0)),X0),
inference(forward_demodulation,[],[f11905,f2]) ).
fof(f11905,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(multiply(X1,inverse(X0)),X0),
inference(superposition,[],[f9508,f2159]) ).
fof(f12111,plain,
! [X0,X1] : add(multiply(X1,X0),inverse(X0)) = add(inverse(X0),X1),
inference(forward_demodulation,[],[f11952,f2798]) ).
fof(f11952,plain,
! [X0,X1] : add(multiply(X1,X0),inverse(X0)) = add(add(inverse(X0),X1),inverse(X0)),
inference(superposition,[],[f78,f9508]) ).
fof(f67332,plain,
! [X0,X1] : add(inverse(add(X0,X1)),X1) = add(inverse(multiply(inverse(X1),X0)),inverse(add(X0,X1))),
inference(superposition,[],[f644,f61636]) ).
fof(f61636,plain,
! [X0,X1] : multiply(add(X1,X0),inverse(multiply(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f61373,f15131]) ).
fof(f15131,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(X0),X1))) = X0,
inference(superposition,[],[f12088,f2]) ).
fof(f12088,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),X1)),X0) = X0,
inference(forward_demodulation,[],[f11921,f12]) ).
fof(f11921,plain,
! [X0,X1] : multiply(multiplicative_identity,X0) = multiply(inverse(multiply(inverse(X0),X1)),X0),
inference(superposition,[],[f9508,f3461]) ).
fof(f3461,plain,
! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X0,X1))),
inference(superposition,[],[f2624,f2793]) ).
fof(f61373,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(X0),X1))) = multiply(add(X1,X0),inverse(multiply(inverse(X0),X1))),
inference(superposition,[],[f9489,f76]) ).
fof(f316134,plain,
! [X0,X1] : inverse(multiply(inverse(inverse(X1)),multiply(X0,X1))) = inverse(multiply(inverse(inverse(X1)),X0)),
inference(forward_demodulation,[],[f315171,f67921]) ).
fof(f315171,plain,
! [X0,X1] : inverse(multiply(inverse(inverse(X1)),multiply(X0,X1))) = add(inverse(add(X0,inverse(X1))),inverse(X1)),
inference(superposition,[],[f67921,f78]) ).
fof(f64004,plain,
! [X0,X1] : add(multiply(X0,X1),inverse(add(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f63741,f13622]) ).
fof(f13622,plain,
! [X0,X1] : add(X0,inverse(add(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f13518,f13]) ).
fof(f13518,plain,
! [X0,X1] : add(X0,additive_identity) = add(X0,inverse(add(inverse(X0),X1))),
inference(superposition,[],[f2060,f12462]) ).
fof(f12462,plain,
! [X0,X1] : additive_identity = multiply(X0,inverse(add(X0,X1))),
inference(superposition,[],[f12132,f2497]) ).
fof(f2060,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f2059,f14]) ).
fof(f2059,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(add(additive_identity,inverse(X0)),X1)),
inference(forward_demodulation,[],[f2058,f1733]) ).
fof(f2058,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(add(multiply(additive_identity,additive_identity),inverse(X0)),X1)),
inference(forward_demodulation,[],[f1949,f12]) ).
fof(f1949,plain,
! [X0,X1] : add(X0,multiply(add(multiply(additive_identity,additive_identity),inverse(X0)),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[],[f4,f314]) ).
fof(f314,plain,
! [X0] : multiplicative_identity = add(X0,add(multiply(additive_identity,additive_identity),inverse(X0))),
inference(forward_demodulation,[],[f313,f7]) ).
fof(f313,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,add(multiply(additive_identity,additive_identity),inverse(X0))),
inference(forward_demodulation,[],[f299,f1]) ).
fof(f299,plain,
! [X0] : add(inverse(X0),X0) = add(X0,add(multiply(additive_identity,additive_identity),inverse(X0))),
inference(superposition,[],[f191,f273]) ).
fof(f63741,plain,
! [X0,X1] : add(X0,inverse(add(inverse(X0),X1))) = add(multiply(X0,X1),inverse(add(inverse(X0),X1))),
inference(superposition,[],[f78,f63182]) ).
fof(f63182,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
inference(superposition,[],[f27370,f663]) ).
fof(f15,axiom,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO008-2 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 14:23:08 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (22512)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (22515)WARNING: value z3 for option sas not known
% 0.22/0.38 % (22514)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (22513)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (22516)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (22515)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39 % (22517)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (22519)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 % (22518)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.40 TRYING [3]
% 0.22/0.41 TRYING [4]
% 0.22/0.44 TRYING [4]
% 0.22/0.45 TRYING [5]
% 1.36/0.55 TRYING [6]
% 1.36/0.59 TRYING [5]
% 2.85/0.79 TRYING [7]
% 5.39/1.13 TRYING [6]
% 6.40/1.31 TRYING [8]
% 7.72/1.48 TRYING [1]
% 7.72/1.48 TRYING [2]
% 7.72/1.49 TRYING [3]
% 7.72/1.50 TRYING [4]
% 7.72/1.53 TRYING [5]
% 8.49/1.62 TRYING [6]
% 10.47/1.89 TRYING [7]
% 13.94/2.35 TRYING [9]
% 15.32/2.56 TRYING [8]
% 23.99/3.83 TRYING [7]
% 29.44/4.59 TRYING [9]
% 52.68/7.89 % (22519)First to succeed.
% 52.68/7.90 % (22519)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22512"
% 52.68/7.90 % (22519)Refutation found. Thanks to Tanya!
% 52.68/7.90 % SZS status Unsatisfiable for theBenchmark
% 52.68/7.90 % SZS output start Proof for theBenchmark
% See solution above
% 52.68/7.90 % (22519)------------------------------
% 52.68/7.90 % (22519)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 52.68/7.90 % (22519)Termination reason: Refutation
% 52.68/7.90
% 52.68/7.90 % (22519)Memory used [KB]: 77964
% 52.68/7.90 % (22519)Time elapsed: 7.512 s
% 52.68/7.90 % (22519)Instructions burned: 20040 (million)
% 52.68/7.90 % (22512)Success in time 7.512 s
%------------------------------------------------------------------------------