TSTP Solution File: BOO007-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : BOO007-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 : Tue Apr 30 10:41:59 EDT 2024

% Result   : Unsatisfiable 35.34s 5.41s
% Output   : Refutation 35.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   85 (  85 unt;   0 def)
%            Number of atoms       :   85 (  84 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    5 (   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   :  173 ( 173   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f132208,plain,
    $false,
    inference(trivial_inequality_removal,[],[f131965]) ).

fof(f131965,plain,
    multiply(a,multiply(b,c)) != multiply(a,multiply(b,c)),
    inference(superposition,[],[f15,f126772]) ).

fof(f126772,plain,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(forward_demodulation,[],[f126771,f778]) ).

fof(f778,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,add(inverse(X0),X1)),
    inference(forward_demodulation,[],[f726,f14]) ).

fof(f14,axiom,
    ! [X0] : add(additive_identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).

fof(f726,plain,
    ! [X0,X1] : add(additive_identity,multiply(X0,X1)) = multiply(X0,add(inverse(X0),X1)),
    inference(superposition,[],[f6,f9]) ).

fof(f9,axiom,
    ! [X0] : multiply(X0,inverse(X0)) = additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).

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(f126771,plain,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,add(inverse(X0),multiply(X1,X2))),
    inference(forward_demodulation,[],[f126770,f7315]) ).

fof(f7315,plain,
    ! [X2,X0,X1] : add(inverse(X0),multiply(X1,X2)) = add(inverse(X0),multiply(multiply(X1,X0),X2)),
    inference(forward_demodulation,[],[f7236,f4]) ).

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(f7236,plain,
    ! [X2,X0,X1] : multiply(add(inverse(X0),X1),add(inverse(X0),X2)) = add(inverse(X0),multiply(multiply(X1,X0),X2)),
    inference(superposition,[],[f4,f165]) ).

fof(f165,plain,
    ! [X0,X1] : add(inverse(X0),X1) = add(inverse(X0),multiply(X1,X0)),
    inference(forward_demodulation,[],[f147,f11]) ).

fof(f11,axiom,
    ! [X0] : multiply(X0,multiplicative_identity) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).

fof(f147,plain,
    ! [X0,X1] : add(inverse(X0),multiply(X1,X0)) = multiply(add(inverse(X0),X1),multiplicative_identity),
    inference(superposition,[],[f4,f8]) ).

fof(f8,axiom,
    ! [X0] : multiplicative_identity = add(inverse(X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).

fof(f126770,plain,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,add(inverse(X0),multiply(multiply(X1,X0),X2))),
    inference(forward_demodulation,[],[f125867,f43250]) ).

fof(f43250,plain,
    ! [X2,X3,X0,X1] : multiply(multiply(X0,X1),X3) = multiply(multiply(X0,X1),add(multiply(inverse(X0),X2),X3)),
    inference(forward_demodulation,[],[f43141,f14]) ).

fof(f43141,plain,
    ! [X2,X3,X0,X1] : add(additive_identity,multiply(multiply(X0,X1),X3)) = multiply(multiply(X0,X1),add(multiply(inverse(X0),X2),X3)),
    inference(superposition,[],[f6,f7949]) ).

fof(f7949,plain,
    ! [X2,X0,X1] : additive_identity = multiply(multiply(X0,X2),multiply(inverse(X0),X1)),
    inference(superposition,[],[f1183,f2212]) ).

fof(f2212,plain,
    ! [X0,X1] : multiply(X0,inverse(multiply(inverse(X0),X1))) = X0,
    inference(forward_demodulation,[],[f2157,f11]) ).

fof(f2157,plain,
    ! [X0,X1] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(multiply(inverse(X0),X1))),
    inference(superposition,[],[f778,f1480]) ).

fof(f1480,plain,
    ! [X0,X1] : multiplicative_identity = add(X0,inverse(multiply(X0,X1))),
    inference(superposition,[],[f1242,f451]) ).

fof(f451,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
    inference(backward_demodulation,[],[f130,f446]) ).

fof(f446,plain,
    ! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
    inference(backward_demodulation,[],[f162,f445]) ).

fof(f445,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
    inference(forward_demodulation,[],[f444,f12]) ).

fof(f12,axiom,
    ! [X0] : multiply(multiplicative_identity,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).

fof(f444,plain,
    ! [X0,X1] : multiply(multiplicative_identity,X0) = add(X0,multiply(X1,X0)),
    inference(forward_demodulation,[],[f413,f98]) ).

fof(f98,plain,
    ! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
    inference(forward_demodulation,[],[f83,f8]) ).

fof(f83,plain,
    ! [X0] : add(inverse(X0),X0) = add(multiplicative_identity,X0),
    inference(superposition,[],[f76,f11]) ).

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(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(f413,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
    inference(superposition,[],[f5,f12]) ).

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(f162,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(X0,add(X0,X1)),
    inference(forward_demodulation,[],[f140,f2]) ).

fof(f2,axiom,
    ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).

fof(f140,plain,
    ! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
    inference(superposition,[],[f4,f97]) ).

fof(f97,plain,
    ! [X0] : add(X0,X0) = X0,
    inference(forward_demodulation,[],[f82,f14]) ).

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(f130,plain,
    ! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
    inference(superposition,[],[f4,f97]) ).

fof(f1242,plain,
    ! [X0,X1] : multiplicative_identity = add(add(X1,X0),inverse(X0)),
    inference(superposition,[],[f601,f1188]) ).

fof(f1188,plain,
    ! [X0] : inverse(inverse(X0)) = X0,
    inference(backward_demodulation,[],[f579,f1187]) ).

fof(f1187,plain,
    ! [X0] : multiply(inverse(inverse(X0)),X0) = X0,
    inference(forward_demodulation,[],[f1144,f12]) ).

fof(f1144,plain,
    ! [X0] : multiply(multiplicative_identity,X0) = multiply(inverse(inverse(X0)),X0),
    inference(superposition,[],[f443,f7]) ).

fof(f7,axiom,
    ! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).

fof(f443,plain,
    ! [X0,X1] : multiply(X1,X0) = multiply(add(inverse(X0),X1),X0),
    inference(forward_demodulation,[],[f412,f14]) ).

fof(f412,plain,
    ! [X0,X1] : add(additive_identity,multiply(X1,X0)) = multiply(add(inverse(X0),X1),X0),
    inference(superposition,[],[f5,f10]) ).

fof(f579,plain,
    ! [X0] : inverse(inverse(X0)) = multiply(inverse(inverse(X0)),X0),
    inference(superposition,[],[f456,f171]) ).

fof(f171,plain,
    ! [X0] : add(X0,inverse(inverse(X0))) = X0,
    inference(superposition,[],[f99,f1]) ).

fof(f1,axiom,
    ! [X0,X1] : add(X0,X1) = add(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).

fof(f99,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(f456,plain,
    ! [X0,X1] : multiply(X0,add(X1,X0)) = X0,
    inference(backward_demodulation,[],[f62,f447]) ).

fof(f447,plain,
    ! [X0,X1] : add(multiply(additive_identity,X0),X1) = X1,
    inference(backward_demodulation,[],[f356,f446]) ).

fof(f356,plain,
    ! [X0,X1] : add(multiply(additive_identity,X0),X1) = multiply(X1,add(X1,X0)),
    inference(superposition,[],[f62,f1]) ).

fof(f62,plain,
    ! [X0,X1] : add(multiply(additive_identity,X1),X0) = multiply(X0,add(X1,X0)),
    inference(superposition,[],[f3,f14]) ).

fof(f601,plain,
    ! [X0,X1] : multiplicative_identity = add(add(X1,inverse(X0)),X0),
    inference(forward_demodulation,[],[f595,f7]) ).

fof(f595,plain,
    ! [X0,X1] : add(X0,inverse(X0)) = add(add(X1,inverse(X0)),X0),
    inference(superposition,[],[f88,f456]) ).

fof(f88,plain,
    ! [X0,X1] : add(X1,X0) = add(X0,multiply(inverse(X0),X1)),
    inference(superposition,[],[f76,f1]) ).

fof(f1183,plain,
    ! [X2,X0,X1] : additive_identity = multiply(multiply(multiply(X1,inverse(X0)),X2),X0),
    inference(forward_demodulation,[],[f1182,f9]) ).

fof(f1182,plain,
    ! [X2,X0,X1] : multiply(X0,inverse(X0)) = multiply(multiply(multiply(X1,inverse(X0)),X2),X0),
    inference(forward_demodulation,[],[f1141,f2]) ).

fof(f1141,plain,
    ! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(multiply(multiply(X1,inverse(X0)),X2),X0),
    inference(superposition,[],[f443,f540]) ).

fof(f540,plain,
    ! [X2,X0,X1] : add(X0,multiply(multiply(X1,X0),X2)) = X0,
    inference(forward_demodulation,[],[f531,f446]) ).

fof(f531,plain,
    ! [X2,X0,X1] : add(X0,multiply(multiply(X1,X0),X2)) = multiply(X0,add(X0,X2)),
    inference(superposition,[],[f4,f445]) ).

fof(f125867,plain,
    ! [X2,X0,X1] : multiply(X0,add(inverse(X0),multiply(multiply(X1,X0),X2))) = multiply(multiply(X0,X1),add(multiply(inverse(X0),X0),X2)),
    inference(superposition,[],[f1125,f1179]) ).

fof(f1179,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(add(inverse(X0),X1),X0),
    inference(forward_demodulation,[],[f1139,f1178]) ).

fof(f1178,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X1,inverse(inverse(X0))),X0),
    inference(forward_demodulation,[],[f1177,f792]) ).

fof(f792,plain,
    ! [X0,X1] : multiply(X0,X1) = multiply(X0,add(X1,inverse(X0))),
    inference(forward_demodulation,[],[f741,f13]) ).

fof(f13,axiom,
    ! [X0] : add(X0,additive_identity) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).

fof(f741,plain,
    ! [X0,X1] : add(multiply(X0,X1),additive_identity) = multiply(X0,add(X1,inverse(X0))),
    inference(superposition,[],[f6,f9]) ).

fof(f1177,plain,
    ! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(multiply(X1,inverse(inverse(X0))),X0),
    inference(forward_demodulation,[],[f1138,f2]) ).

fof(f1138,plain,
    ! [X0,X1] : multiply(add(X1,inverse(X0)),X0) = multiply(multiply(X1,inverse(inverse(X0))),X0),
    inference(superposition,[],[f443,f206]) ).

fof(f206,plain,
    ! [X0,X1] : add(X0,X1) = add(X1,multiply(X0,inverse(X1))),
    inference(superposition,[],[f79,f1]) ).

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(f1139,plain,
    ! [X0,X1] : multiply(add(inverse(X0),X1),X0) = multiply(multiply(X1,inverse(inverse(X0))),X0),
    inference(superposition,[],[f443,f163]) ).

fof(f163,plain,
    ! [X0,X1] : add(X0,X1) = add(X0,multiply(X1,inverse(X0))),
    inference(forward_demodulation,[],[f143,f11]) ).

fof(f143,plain,
    ! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
    inference(superposition,[],[f4,f7]) ).

fof(f1125,plain,
    ! [X2,X3,X0,X1] : multiply(multiply(add(X0,X2),X1),add(multiply(X0,X1),X3)) = multiply(X1,add(X0,multiply(multiply(X2,X1),X3))),
    inference(backward_demodulation,[],[f437,f1124]) ).

fof(f1124,plain,
    ! [X2,X3,X0,X1] : multiply(X0,add(X3,multiply(multiply(X1,X0),X2))) = add(multiply(X3,X0),multiply(multiply(X1,X0),X2)),
    inference(forward_demodulation,[],[f1109,f2]) ).

fof(f1109,plain,
    ! [X2,X3,X0,X1] : add(multiply(X3,X0),multiply(multiply(X1,X0),X2)) = multiply(add(X3,multiply(multiply(X1,X0),X2)),X0),
    inference(superposition,[],[f3,f540]) ).

fof(f437,plain,
    ! [X2,X3,X0,X1] : add(multiply(X0,X1),multiply(multiply(X2,X1),X3)) = multiply(multiply(add(X0,X2),X1),add(multiply(X0,X1),X3)),
    inference(superposition,[],[f4,f5]) ).

fof(f15,axiom,
    multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : BOO007-2 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 02:18:35 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (27970)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (27977)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)
% 0.14/0.37  % (27973)WARNING: value z3 for option sas not known
% 0.14/0.37  % (27971)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (27972)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (27974)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (27973)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)
% 0.14/0.37  % (27975)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)
% 0.14/0.37  % (27976)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)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [4]
% 0.20/0.43  TRYING [4]
% 0.20/0.45  TRYING [5]
% 1.71/0.60  TRYING [6]
% 1.71/0.62  TRYING [5]
% 3.80/0.91  TRYING [7]
% 6.28/1.28  TRYING [6]
% 7.80/1.47  TRYING [1]
% 7.80/1.47  TRYING [2]
% 7.80/1.47  TRYING [3]
% 7.80/1.49  TRYING [4]
% 8.37/1.54  TRYING [5]
% 9.28/1.67  TRYING [8]
% 9.28/1.69  TRYING [6]
% 12.24/2.09  TRYING [7]
% 19.46/3.17  TRYING [8]
% 21.06/3.39  TRYING [9]
% 35.09/5.39  % (27976)First to succeed.
% 35.34/5.41  % (27976)Refutation found. Thanks to Tanya!
% 35.34/5.41  % SZS status Unsatisfiable for theBenchmark
% 35.34/5.41  % SZS output start Proof for theBenchmark
% See solution above
% 35.34/5.41  % (27976)------------------------------
% 35.34/5.41  % (27976)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 35.34/5.41  % (27976)Termination reason: Refutation
% 35.34/5.41  
% 35.34/5.41  % (27976)Memory used [KB]: 39954
% 35.34/5.41  % (27976)Time elapsed: 5.031 s
% 35.34/5.41  % (27976)Instructions burned: 9789 (million)
% 35.34/5.41  % (27976)------------------------------
% 35.34/5.41  % (27976)------------------------------
% 35.34/5.41  % (27970)Success in time 5.002 s
%------------------------------------------------------------------------------