TSTP Solution File: GRP213-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n014.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 : Wed Aug 31 16:20:54 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 34
% Syntax : Number of formulae : 164 ( 15 unt; 0 def)
% Number of atoms : 642 ( 198 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 958 ( 480 ~; 464 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f57,f62,f68,f69,f70,f76,f82,f83,f84,f85,f86,f87,f89,f93,f94,f107,f112,f146,f307,f329,f348,f381,f580,f620,f642,f662]) ).
fof(f662,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f661]) ).
fof(f661,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f653,f350]) ).
fof(f350,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f245,f256]) ).
fof(f256,plain,
! [X6] : inverse(inverse(X6)) = X6,
inference(forward_demodulation,[],[f253,f230]) ).
fof(f230,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f214,f213]) ).
fof(f213,plain,
! [X4] : multiply(inverse(inverse(X4)),identity) = X4,
inference(superposition,[],[f130,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f130,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f122,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f122,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = multiply(identity,X7),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f214,plain,
! [X6,X5] : multiply(inverse(inverse(X5)),X6) = multiply(X5,X6),
inference(superposition,[],[f130,f130]) ).
fof(f253,plain,
! [X6] : inverse(inverse(X6)) = multiply(X6,identity),
inference(superposition,[],[f214,f230]) ).
fof(f245,plain,
identity = inverse(inverse(inverse(identity))),
inference(superposition,[],[f230,f220]) ).
fof(f220,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f130,f213]) ).
fof(f653,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f650]) ).
fof(f650,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f645,f1]) ).
fof(f645,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f644,f584]) ).
fof(f584,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f583,f350]) ).
fof(f583,plain,
( sk_c7 = inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f38,f361]) ).
fof(f361,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[],[f56,f357]) ).
fof(f357,plain,
( identity = multiply(sk_c2,sk_c3)
| ~ spl0_3 ),
inference(superposition,[],[f236,f43]) ).
fof(f43,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl0_3
<=> sk_c3 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f236,plain,
! [X2] : identity = multiply(X2,inverse(X2)),
inference(superposition,[],[f2,f214]) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f54,plain,
( spl0_6
<=> sk_c8 = multiply(sk_c2,sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f36,plain,
( spl0_2
<=> sk_c7 = inverse(sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f644,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f643,f361]) ).
fof(f643,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,identity) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f361]) ).
fof(f103,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f102,plain,
( spl0_13
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f642,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f641,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f632,f350]) ).
fof(f632,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f629]) ).
fof(f629,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(superposition,[],[f624,f230]) ).
fof(f624,plain,
( ! [X8] :
( identity != multiply(identity,X8)
| identity != inverse(X8) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f623,f584]) ).
fof(f623,plain,
( ! [X8] :
( sk_c7 != multiply(identity,X8)
| identity != inverse(X8) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f622,f230]) ).
fof(f622,plain,
( ! [X8] :
( sk_c7 != multiply(identity,multiply(X8,identity))
| identity != inverse(X8) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f621,f361]) ).
fof(f621,plain,
( ! [X8] :
( sk_c8 != inverse(X8)
| sk_c7 != multiply(identity,multiply(X8,identity)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f100,f361]) ).
fof(f100,plain,
( ! [X8] :
( sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != inverse(X8) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f99,plain,
( spl0_12
<=> ! [X8] :
( sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != inverse(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f620,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f619,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f614,f350]) ).
fof(f614,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f608]) ).
fof(f608,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(superposition,[],[f588,f1]) ).
fof(f588,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(backward_demodulation,[],[f573,f584]) ).
fof(f573,plain,
( ! [X6] :
( identity != multiply(X6,sk_c7)
| identity != inverse(X6) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f548,f361]) ).
fof(f548,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c8 != multiply(X6,sk_c7) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f106,f361]) ).
fof(f106,plain,
( ! [X6] :
( sk_c8 != inverse(X6)
| sk_c8 != multiply(X6,sk_c7) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f105,plain,
( spl0_14
<=> ! [X6] :
( sk_c8 != multiply(X6,sk_c7)
| sk_c8 != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f580,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f579,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(subsumption_resolution,[],[f578,f575]) ).
fof(f575,plain,
( identity != sk_c7
| spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f574,f350]) ).
fof(f574,plain,
( sk_c7 != inverse(identity)
| spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f37,f361]) ).
fof(f37,plain,
( sk_c7 != inverse(sk_c8)
| spl0_2 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f578,plain,
( identity = sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f577,f424]) ).
fof(f424,plain,
( identity = sk_c1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f419,f350]) ).
fof(f419,plain,
( sk_c1 = inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f256,f364]) ).
fof(f364,plain,
( identity = inverse(sk_c1)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(backward_demodulation,[],[f66,f361]) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl0_8
<=> sk_c8 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f577,plain,
( sk_c1 = sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f576,f230]) ).
fof(f576,plain,
( sk_c7 = multiply(sk_c1,identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f34,f361]) ).
fof(f34,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f32,plain,
( spl0_1
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f381,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f380,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f378,f350]) ).
fof(f378,plain,
( identity != inverse(identity)
| spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f353,f361]) ).
fof(f353,plain,
( sk_c8 != inverse(sk_c8)
| spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f37,f137]) ).
fof(f137,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f75,f135]) ).
fof(f135,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f131,f52]) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f50,plain,
( spl0_5
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f131,plain,
( ! [X9] : multiply(sk_c8,multiply(sk_c5,X9)) = X9
| ~ spl0_7 ),
inference(forward_demodulation,[],[f124,f1]) ).
fof(f124,plain,
( ! [X9] : multiply(sk_c8,multiply(sk_c5,X9)) = multiply(identity,X9)
| ~ spl0_7 ),
inference(superposition,[],[f3,f118]) ).
fof(f118,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f2,f61]) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl0_7
<=> sk_c8 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f75,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f73,plain,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f348,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f347]) ).
fof(f347,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(subsumption_resolution,[],[f341,f168]) ).
fof(f168,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(backward_demodulation,[],[f138,f157]) ).
fof(f157,plain,
( identity = sk_c8
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f155,f141]) ).
fof(f141,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f117,f137]) ).
fof(f117,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_2 ),
inference(superposition,[],[f2,f38]) ).
fof(f155,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f132,f139]) ).
fof(f139,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f47,f137]) ).
fof(f47,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f45,plain,
( spl0_4
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f132,plain,
( ! [X10] : multiply(sk_c8,multiply(sk_c4,X10)) = X10
| ~ spl0_10 ),
inference(forward_demodulation,[],[f125,f1]) ).
fof(f125,plain,
( ! [X10] : multiply(identity,X10) = multiply(sk_c8,multiply(sk_c4,X10))
| ~ spl0_10 ),
inference(superposition,[],[f3,f119]) ).
fof(f119,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f2,f80]) ).
fof(f80,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f138,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f38,f137]) ).
fof(f341,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f337]) ).
fof(f337,plain,
( identity != inverse(identity)
| identity != identity
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(superposition,[],[f332,f1]) ).
fof(f332,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f331,f157]) ).
fof(f331,plain,
( ! [X6] :
( sk_c8 != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f330,f167]) ).
fof(f167,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(backward_demodulation,[],[f137,f157]) ).
fof(f330,plain,
( ! [X6] :
( identity != inverse(X6)
| sk_c8 != multiply(X6,sk_c7) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[],[f106,f157]) ).
fof(f329,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f328,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f321,f168]) ).
fof(f321,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f317]) ).
fof(f317,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(superposition,[],[f312,f1]) ).
fof(f312,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f311,f167]) ).
fof(f311,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f310,f157]) ).
fof(f310,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c7 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f157]) ).
fof(f307,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f306]) ).
fof(f306,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(subsumption_resolution,[],[f302,f256]) ).
fof(f302,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f297]) ).
fof(f297,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[],[f240,f236]) ).
fof(f240,plain,
( ! [X8] :
( identity != multiply(identity,X8)
| identity != inverse(X8) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(backward_demodulation,[],[f176,f230]) ).
fof(f176,plain,
( ! [X8] :
( identity != inverse(X8)
| identity != multiply(identity,multiply(X8,identity)) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f174,f157]) ).
fof(f174,plain,
( ! [X8] :
( sk_c8 != multiply(sk_c8,multiply(X8,sk_c8))
| identity != inverse(X8) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(backward_demodulation,[],[f149,f157]) ).
fof(f149,plain,
( ! [X8] :
( sk_c8 != inverse(X8)
| sk_c8 != multiply(sk_c8,multiply(X8,sk_c8)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f100,f137]) ).
fof(f146,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f145,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(subsumption_resolution,[],[f139,f115]) ).
fof(f115,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f97,f80]) ).
fof(f97,plain,
( ! [X4] : sk_c8 != multiply(X4,inverse(X4))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl0_11
<=> ! [X4] : sk_c8 != multiply(X4,inverse(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f112,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f111,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_11 ),
inference(subsumption_resolution,[],[f108,f56]) ).
fof(f108,plain,
( sk_c8 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f97,f43]) ).
fof(f107,plain,
( spl0_11
| spl0_12
| ~ spl0_2
| spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f105,f102,f36,f99,f96]) ).
fof(f30,plain,
! [X3,X8,X6,X4] :
( sk_c8 != multiply(X6,sk_c7)
| sk_c8 != inverse(X3)
| sk_c7 != inverse(sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != inverse(X6)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X8) ),
inference(equality_resolution,[],[f29]) ).
fof(f29,plain,
! [X3,X8,X6,X4,X5] :
( sk_c8 != inverse(X6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != inverse(X8)
| sk_c7 != inverse(sk_c8) ),
inference(equality_resolution,[],[f28]) ).
fof(f28,axiom,
! [X3,X8,X6,X7,X4,X5] :
( sk_c8 != inverse(X6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(sk_c8,X7)
| multiply(X8,sk_c8) != X7
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != inverse(X8)
| sk_c7 != inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f94,plain,
( spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f27,f41,f59]) ).
fof(f27,axiom,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f93,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f17,f54,f78]) ).
fof(f17,axiom,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f89,plain,
( spl0_1
| spl0_9 ),
inference(avatar_split_clause,[],[f7,f73,f32]) ).
fof(f7,axiom,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f87,plain,
( spl0_10
| spl0_3 ),
inference(avatar_split_clause,[],[f23,f41,f78]) ).
fof(f23,axiom,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f86,plain,
( spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f54,f36]) ).
fof(f16,axiom,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f85,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f25,f73,f41]) ).
fof(f25,axiom,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f84,plain,
( spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f9,f59,f32]) ).
fof(f9,axiom,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f83,plain,
( spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f8,f32,f50]) ).
fof(f8,axiom,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f82,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f22,f41,f36]) ).
fof(f22,axiom,
( sk_c3 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f76,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f19,f54,f73]) ).
fof(f19,axiom,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f70,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f26,f41,f50]) ).
fof(f26,axiom,
( sk_c3 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f69,plain,
( spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f54,f45]) ).
fof(f18,axiom,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f68,plain,
( spl0_8
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f36,f64]) ).
fof(f10,axiom,
( sk_c7 = inverse(sk_c8)
| sk_c8 = inverse(sk_c1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f62,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f21,f59,f54]) ).
fof(f21,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f57,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f54,f50]) ).
fof(f20,axiom,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f48,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f24,f45,f41]) ).
fof(f24,axiom,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c3 = inverse(sk_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 22:22:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (28754)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50 % (28765)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.50 % (28777)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.51 % (28763)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (28764)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51 % (28754)First to succeed.
% 0.19/0.52 % (28754)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (28754)------------------------------
% 0.19/0.52 % (28754)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (28754)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (28754)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (28754)Memory used [KB]: 5756
% 0.19/0.52 % (28754)Time elapsed: 0.107 s
% 0.19/0.52 % (28754)Instructions burned: 21 (million)
% 0.19/0.52 % (28754)------------------------------
% 0.19/0.52 % (28754)------------------------------
% 0.19/0.52 % (28752)Success in time 0.166 s
%------------------------------------------------------------------------------