TSTP Solution File: BOO007-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO007-2 : 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 18:58:44 EDT 2024
% Result : Unsatisfiable 36.19s 5.54s
% Output : Refutation 36.19s
% 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
% 0.00/0.12 % Problem : BOO007-2 : TPTP v8.2.0. Released v1.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n019.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 : Sat May 18 14:24:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (24759)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (24762)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (24764)WARNING: value z3 for option sas not known
% 0.15/0.38 % (24763)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (24766)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)
% 0.15/0.38 % (24765)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (24768)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)
% 0.15/0.38 % (24767)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)
% 0.15/0.38 % (24764)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [4]
% 0.22/0.43 TRYING [4]
% 0.22/0.44 TRYING [5]
% 1.55/0.58 TRYING [6]
% 1.74/0.59 TRYING [5]
% 4.26/0.95 TRYING [7]
% 6.30/1.31 TRYING [6]
% 7.86/1.48 TRYING [1]
% 7.86/1.48 TRYING [2]
% 7.86/1.48 TRYING [3]
% 7.86/1.50 TRYING [4]
% 8.37/1.55 TRYING [5]
% 9.03/1.70 TRYING [6]
% 10.37/1.83 TRYING [8]
% 12.19/2.09 TRYING [7]
% 19.52/3.17 TRYING [8]
% 22.64/3.59 TRYING [9]
% 35.31/5.46 TRYING [7]
% 36.19/5.52 % (24767)First to succeed.
% 36.19/5.53 % (24767)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24759"
% 36.19/5.54 % (24767)Refutation found. Thanks to Tanya!
% 36.19/5.54 % SZS status Unsatisfiable for theBenchmark
% 36.19/5.54 % SZS output start Proof for theBenchmark
% See solution above
% 36.19/5.54 % (24767)------------------------------
% 36.19/5.54 % (24767)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 36.19/5.54 % (24767)Termination reason: Refutation
% 36.19/5.54
% 36.19/5.54 % (24767)Memory used [KB]: 39955
% 36.19/5.54 % (24767)Time elapsed: 5.156 s
% 36.19/5.54 % (24767)Instructions burned: 9788 (million)
% 36.19/5.54 % (24759)Success in time 5.169 s
%------------------------------------------------------------------------------