TSTP Solution File: GRP344-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP344-1 : 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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 16:21:22 EDT 2022
% Result : Unsatisfiable 1.37s 0.53s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 40
% Syntax : Number of formulae : 194 ( 8 unt; 0 def)
% Number of atoms : 641 ( 224 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 908 ( 461 ~; 424 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f578,plain,
$false,
inference(avatar_sat_refutation,[],[f36,f44,f52,f66,f71,f81,f83,f84,f94,f95,f96,f97,f101,f102,f103,f105,f144,f153,f182,f247,f249,f315,f338,f355,f362,f437,f438,f457,f492,f503,f533,f535,f577]) ).
fof(f577,plain,
( ~ spl3_2
| spl3_16
| ~ spl3_19 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f576,plain,
( $false
| ~ spl3_2
| spl3_16
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f575]) ).
fof(f575,plain,
( identity != identity
| ~ spl3_2
| spl3_16
| ~ spl3_19 ),
inference(superposition,[],[f539,f557]) ).
fof(f557,plain,
( identity = inverse(identity)
| ~ spl3_2
| ~ spl3_19 ),
inference(forward_demodulation,[],[f537,f552]) ).
fof(f552,plain,
( identity = sk_c3
| ~ spl3_2
| ~ spl3_19 ),
inference(forward_demodulation,[],[f550,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f550,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl3_2
| ~ spl3_19 ),
inference(backward_demodulation,[],[f518,f125]) ).
fof(f125,plain,
( identity = sk_c6
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f124,plain,
( spl3_19
<=> identity = sk_c6 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f518,plain,
( sk_c3 = multiply(inverse(sk_c6),identity)
| ~ spl3_2 ),
inference(superposition,[],[f138,f405]) ).
fof(f405,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl3_2 ),
inference(superposition,[],[f2,f35]) ).
fof(f35,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f33,plain,
( spl3_2
<=> sk_c6 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f138,plain,
! [X6,X7] : multiply(inverse(X6),multiply(X6,X7)) = X7,
inference(forward_demodulation,[],[f130,f1]) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f130,plain,
! [X6,X7] : multiply(identity,X7) = multiply(inverse(X6),multiply(X6,X7)),
inference(superposition,[],[f3,f2]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f537,plain,
( identity = inverse(sk_c3)
| ~ spl3_2
| ~ spl3_19 ),
inference(backward_demodulation,[],[f35,f125]) ).
fof(f539,plain,
( identity != inverse(identity)
| spl3_16
| ~ spl3_19 ),
inference(backward_demodulation,[],[f113,f125]) ).
fof(f113,plain,
( sk_c6 != inverse(identity)
| spl3_16 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f111,plain,
( spl3_16
<=> sk_c6 = inverse(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f535,plain,
( ~ spl3_19
| ~ spl3_2
| ~ spl3_10
| ~ spl3_15
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f517,f176,f99,f68,f33,f124]) ).
fof(f68,plain,
( spl3_10
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f99,plain,
( spl3_15
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f176,plain,
( spl3_23
<=> identity = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f517,plain,
( identity != sk_c6
| ~ spl3_2
| ~ spl3_10
| ~ spl3_15
| ~ spl3_23 ),
inference(superposition,[],[f516,f35]) ).
fof(f516,plain,
( identity != inverse(sk_c3)
| ~ spl3_10
| ~ spl3_15
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f512]) ).
fof(f512,plain,
( identity != inverse(sk_c3)
| identity != identity
| ~ spl3_10
| ~ spl3_15
| ~ spl3_23 ),
inference(superposition,[],[f505,f460]) ).
fof(f460,plain,
( identity = multiply(sk_c3,sk_c6)
| ~ spl3_10
| ~ spl3_23 ),
inference(backward_demodulation,[],[f70,f177]) ).
fof(f177,plain,
( identity = sk_c7
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f70,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f505,plain,
( ! [X3] :
( identity != multiply(X3,sk_c6)
| identity != inverse(X3) )
| ~ spl3_15
| ~ spl3_23 ),
inference(forward_demodulation,[],[f504,f177]) ).
fof(f504,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| identity != inverse(X3) )
| ~ spl3_15
| ~ spl3_23 ),
inference(forward_demodulation,[],[f100,f177]) ).
fof(f100,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) )
| ~ spl3_15 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f533,plain,
( spl3_19
| ~ spl3_2
| ~ spl3_8
| ~ spl3_10
| ~ spl3_11
| ~ spl3_17
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f532,f176,f115,f73,f68,f58,f33,f124]) ).
fof(f58,plain,
( spl3_8
<=> sk_c5 = multiply(sk_c4,sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f73,plain,
( spl3_11
<=> sk_c5 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f115,plain,
( spl3_17
<=> sk_c6 = sk_c5 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f532,plain,
( identity = sk_c6
| ~ spl3_2
| ~ spl3_8
| ~ spl3_10
| ~ spl3_11
| ~ spl3_17
| ~ spl3_23 ),
inference(backward_demodulation,[],[f459,f529]) ).
fof(f529,plain,
( ! [X11] : multiply(sk_c6,X11) = X11
| ~ spl3_2
| ~ spl3_8
| ~ spl3_10
| ~ spl3_11
| ~ spl3_17
| ~ spl3_23 ),
inference(forward_demodulation,[],[f523,f482]) ).
fof(f482,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c6,X0)) = X0
| ~ spl3_10
| ~ spl3_23 ),
inference(forward_demodulation,[],[f481,f1]) ).
fof(f481,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c3,multiply(sk_c6,X0))
| ~ spl3_10
| ~ spl3_23 ),
inference(superposition,[],[f3,f460]) ).
fof(f523,plain,
( ! [X11] : multiply(sk_c6,X11) = multiply(sk_c3,multiply(sk_c6,X11))
| ~ spl3_2
| ~ spl3_8
| ~ spl3_11
| ~ spl3_17 ),
inference(backward_demodulation,[],[f467,f521]) ).
fof(f521,plain,
( sk_c3 = sk_c4
| ~ spl3_2
| ~ spl3_11
| ~ spl3_17 ),
inference(backward_demodulation,[],[f390,f518]) ).
fof(f390,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl3_11
| ~ spl3_17 ),
inference(backward_demodulation,[],[f197,f116]) ).
fof(f116,plain,
( sk_c6 = sk_c5
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f197,plain,
( sk_c4 = multiply(inverse(sk_c5),identity)
| ~ spl3_11 ),
inference(superposition,[],[f138,f107]) ).
fof(f107,plain,
( identity = multiply(sk_c5,sk_c4)
| ~ spl3_11 ),
inference(superposition,[],[f2,f75]) ).
fof(f75,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f467,plain,
( ! [X11] : multiply(sk_c6,X11) = multiply(sk_c4,multiply(sk_c6,X11))
| ~ spl3_8
| ~ spl3_17 ),
inference(forward_demodulation,[],[f134,f116]) ).
fof(f134,plain,
( ! [X11] : multiply(sk_c4,multiply(sk_c6,X11)) = multiply(sk_c5,X11)
| ~ spl3_8 ),
inference(superposition,[],[f3,f60]) ).
fof(f60,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f459,plain,
( sk_c6 = multiply(sk_c6,identity)
| ~ spl3_17
| ~ spl3_23 ),
inference(backward_demodulation,[],[f446,f177]) ).
fof(f446,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl3_17 ),
inference(forward_demodulation,[],[f4,f116]) ).
fof(f4,axiom,
multiply(sk_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f503,plain,
( ~ spl3_20
| ~ spl3_3
| ~ spl3_8
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f501,f115,f58,f38,f163]) ).
fof(f163,plain,
( spl3_20
<=> sk_c6 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f38,plain,
( spl3_3
<=> ! [X4] :
( sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f501,plain,
( sk_c6 != inverse(sk_c4)
| ~ spl3_3
| ~ spl3_8
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f498]) ).
fof(f498,plain,
( sk_c6 != sk_c6
| sk_c6 != inverse(sk_c4)
| ~ spl3_3
| ~ spl3_8
| ~ spl3_17 ),
inference(superposition,[],[f493,f442]) ).
fof(f442,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl3_8
| ~ spl3_17 ),
inference(forward_demodulation,[],[f60,f116]) ).
fof(f493,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl3_3
| ~ spl3_17 ),
inference(forward_demodulation,[],[f39,f116]) ).
fof(f39,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f492,plain,
( ~ spl3_2
| ~ spl3_10
| ~ spl3_13
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f491,f176,f88,f68,f33]) ).
fof(f88,plain,
( spl3_13
<=> ! [X5] :
( sk_c6 != inverse(X5)
| sk_c7 != multiply(X5,sk_c6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f491,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl3_10
| ~ spl3_13
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f487]) ).
fof(f487,plain,
( sk_c6 != inverse(sk_c3)
| identity != identity
| ~ spl3_10
| ~ spl3_13
| ~ spl3_23 ),
inference(superposition,[],[f458,f460]) ).
fof(f458,plain,
( ! [X5] :
( identity != multiply(X5,sk_c6)
| sk_c6 != inverse(X5) )
| ~ spl3_13
| ~ spl3_23 ),
inference(backward_demodulation,[],[f89,f177]) ).
fof(f89,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c6)
| sk_c6 != inverse(X5) )
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f457,plain,
( spl3_23
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f456,f115,f176]) ).
fof(f456,plain,
( identity = sk_c7
| ~ spl3_17 ),
inference(forward_demodulation,[],[f455,f2]) ).
fof(f455,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl3_17 ),
inference(forward_demodulation,[],[f194,f116]) ).
fof(f194,plain,
sk_c7 = multiply(inverse(sk_c6),sk_c5),
inference(superposition,[],[f138,f4]) ).
fof(f438,plain,
( ~ spl3_2
| ~ spl3_6
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f435,f115,f78,f68,f63,f50,f33]) ).
fof(f50,plain,
( spl3_6
<=> ! [X6] :
( sk_c5 != multiply(X6,sk_c6)
| sk_c5 != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f63,plain,
( spl3_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f78,plain,
( spl3_12
<=> sk_c6 = inverse(sk_c2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f435,plain,
( sk_c6 != inverse(sk_c3)
| ~ spl3_6
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f434]) ).
fof(f434,plain,
( sk_c6 != inverse(sk_c3)
| sk_c6 != sk_c6
| ~ spl3_6
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12
| ~ spl3_17 ),
inference(superposition,[],[f430,f400]) ).
fof(f400,plain,
( sk_c6 = multiply(sk_c3,sk_c6)
| ~ spl3_9
| ~ spl3_10
| ~ spl3_12 ),
inference(forward_demodulation,[],[f70,f224]) ).
fof(f224,plain,
( sk_c6 = sk_c7
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f194,f217]) ).
fof(f217,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c5)
| ~ spl3_9
| ~ spl3_12 ),
inference(superposition,[],[f138,f204]) ).
fof(f204,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl3_9
| ~ spl3_12 ),
inference(forward_demodulation,[],[f201,f80]) ).
fof(f80,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f201,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl3_9 ),
inference(superposition,[],[f138,f65]) ).
fof(f65,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f430,plain,
( ! [X6] :
( sk_c6 != multiply(X6,sk_c6)
| sk_c6 != inverse(X6) )
| ~ spl3_6
| ~ spl3_17 ),
inference(forward_demodulation,[],[f429,f116]) ).
fof(f429,plain,
( ! [X6] :
( sk_c6 != inverse(X6)
| sk_c5 != multiply(X6,sk_c6) )
| ~ spl3_6
| ~ spl3_17 ),
inference(forward_demodulation,[],[f51,f116]) ).
fof(f51,plain,
( ! [X6] :
( sk_c5 != multiply(X6,sk_c6)
| sk_c5 != inverse(X6) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f437,plain,
( ~ spl3_16
| ~ spl3_6
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f436,f115,f50,f111]) ).
fof(f436,plain,
( sk_c6 != inverse(identity)
| ~ spl3_6
| ~ spl3_17 ),
inference(trivial_inequality_removal,[],[f431]) ).
fof(f431,plain,
( sk_c6 != inverse(identity)
| sk_c6 != sk_c6
| ~ spl3_6
| ~ spl3_17 ),
inference(superposition,[],[f430,f1]) ).
fof(f362,plain,
( spl3_19
| ~ spl3_9
| ~ spl3_12
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f361,f176,f78,f63,f124]) ).
fof(f361,plain,
( identity = sk_c6
| ~ spl3_9
| ~ spl3_12
| ~ spl3_23 ),
inference(forward_demodulation,[],[f224,f177]) ).
fof(f355,plain,
( ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f354,plain,
( $false
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f353]) ).
fof(f353,plain,
( identity != identity
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(superposition,[],[f347,f297]) ).
fof(f297,plain,
( identity = inverse(identity)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_19 ),
inference(backward_demodulation,[],[f281,f292]) ).
fof(f292,plain,
( identity = sk_c1
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_19 ),
inference(forward_demodulation,[],[f286,f2]) ).
fof(f286,plain,
( sk_c1 = multiply(inverse(identity),identity)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_19 ),
inference(backward_demodulation,[],[f236,f125]) ).
fof(f236,plain,
( sk_c1 = multiply(inverse(sk_c6),identity)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f196,f224]) ).
fof(f196,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl3_1 ),
inference(superposition,[],[f138,f146]) ).
fof(f146,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl3_1 ),
inference(superposition,[],[f2,f31]) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f29,plain,
( spl3_1
<=> sk_c7 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f281,plain,
( identity = inverse(sk_c1)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_19 ),
inference(backward_demodulation,[],[f226,f125]) ).
fof(f226,plain,
( sk_c6 = inverse(sk_c1)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f31,f224]) ).
fof(f347,plain,
( identity != inverse(identity)
| ~ spl3_1
| ~ spl3_9
| ~ spl3_12
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f345,f297]) ).
fof(f345,plain,
( identity != inverse(inverse(identity))
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(trivial_inequality_removal,[],[f344]) ).
fof(f344,plain,
( identity != inverse(inverse(identity))
| identity != identity
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(superposition,[],[f341,f2]) ).
fof(f341,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f340,f177]) ).
fof(f340,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c7 != multiply(X3,identity) )
| ~ spl3_15
| ~ spl3_19
| ~ spl3_23 ),
inference(forward_demodulation,[],[f339,f125]) ).
fof(f339,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c7 != multiply(X3,sk_c6) )
| ~ spl3_15
| ~ spl3_23 ),
inference(forward_demodulation,[],[f100,f177]) ).
fof(f338,plain,
( ~ spl3_1
| ~ spl3_6
| ~ spl3_9
| ~ spl3_12
| ~ spl3_17
| ~ spl3_19 ),
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f337,plain,
( $false
| ~ spl3_1
| ~ spl3_6
| ~ spl3_9
| ~ spl3_12
| ~ spl3_17
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f336]) ).
fof(f336,plain,
( identity != identity
| ~ spl3_1
| ~ spl3_6
| ~ spl3_9
| ~ spl3_12
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f330,f297]) ).
fof(f330,plain,
( identity != inverse(identity)
| ~ spl3_6
| ~ spl3_17
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f326]) ).
fof(f326,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl3_6
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f321,f1]) ).
fof(f321,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl3_6
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_demodulation,[],[f320,f304]) ).
fof(f304,plain,
( identity = sk_c5
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_demodulation,[],[f116,f125]) ).
fof(f320,plain,
( ! [X6] :
( sk_c5 != inverse(X6)
| identity != multiply(X6,identity) )
| ~ spl3_6
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_demodulation,[],[f319,f304]) ).
fof(f319,plain,
( ! [X6] :
( sk_c5 != multiply(X6,identity)
| sk_c5 != inverse(X6) )
| ~ spl3_6
| ~ spl3_19 ),
inference(forward_demodulation,[],[f51,f125]) ).
fof(f315,plain,
( ~ spl3_23
| ~ spl3_1
| ~ spl3_7
| ~ spl3_13
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f277,f124,f88,f54,f29,f176]) ).
fof(f54,plain,
( spl3_7
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f277,plain,
( identity != sk_c7
| ~ spl3_1
| ~ spl3_7
| ~ spl3_13
| ~ spl3_19 ),
inference(backward_demodulation,[],[f180,f125]) ).
fof(f180,plain,
( sk_c6 != sk_c7
| ~ spl3_1
| ~ spl3_7
| ~ spl3_13 ),
inference(superposition,[],[f160,f31]) ).
fof(f160,plain,
( sk_c6 != inverse(sk_c1)
| ~ spl3_7
| ~ spl3_13 ),
inference(trivial_inequality_removal,[],[f157]) ).
fof(f157,plain,
( sk_c6 != inverse(sk_c1)
| sk_c7 != sk_c7
| ~ spl3_7
| ~ spl3_13 ),
inference(superposition,[],[f89,f56]) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f249,plain,
( spl3_19
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f248,f78,f63,f54,f29,f124]) ).
fof(f248,plain,
( identity = sk_c6
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(forward_demodulation,[],[f239,f2]) ).
fof(f239,plain,
( sk_c6 = multiply(inverse(sk_c6),sk_c6)
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f207,f224]) ).
fof(f207,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl3_1
| ~ spl3_7 ),
inference(superposition,[],[f138,f203]) ).
fof(f203,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl3_1
| ~ spl3_7 ),
inference(forward_demodulation,[],[f198,f31]) ).
fof(f198,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl3_7 ),
inference(superposition,[],[f138,f56]) ).
fof(f247,plain,
( spl3_17
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f246,f78,f63,f54,f29,f115]) ).
fof(f246,plain,
( sk_c6 = sk_c5
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f204,f238]) ).
fof(f238,plain,
( sk_c6 = multiply(sk_c6,sk_c6)
| ~ spl3_1
| ~ spl3_7
| ~ spl3_9
| ~ spl3_12 ),
inference(backward_demodulation,[],[f203,f224]) ).
fof(f182,plain,
( ~ spl3_17
| ~ spl3_11
| spl3_20 ),
inference(avatar_split_clause,[],[f181,f163,f73,f115]) ).
fof(f181,plain,
( sk_c6 != sk_c5
| ~ spl3_11
| spl3_20 ),
inference(superposition,[],[f165,f75]) ).
fof(f165,plain,
( sk_c6 != inverse(sk_c4)
| spl3_20 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f153,plain,
( ~ spl3_12
| ~ spl3_3
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f152,f63,f38,f78]) ).
fof(f152,plain,
( sk_c6 != inverse(sk_c2)
| ~ spl3_3
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f150]) ).
fof(f150,plain,
( sk_c6 != inverse(sk_c2)
| sk_c6 != sk_c6
| ~ spl3_3
| ~ spl3_9 ),
inference(superposition,[],[f39,f65]) ).
fof(f144,plain,
( spl3_17
| ~ spl3_2
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f143,f68,f33,f115]) ).
fof(f143,plain,
( sk_c6 = sk_c5
| ~ spl3_2
| ~ spl3_10 ),
inference(backward_demodulation,[],[f4,f141]) ).
fof(f141,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl3_2
| ~ spl3_10 ),
inference(superposition,[],[f136,f70]) ).
fof(f136,plain,
( ! [X9] : multiply(sk_c6,multiply(sk_c3,X9)) = X9
| ~ spl3_2 ),
inference(forward_demodulation,[],[f132,f1]) ).
fof(f132,plain,
( ! [X9] : multiply(identity,X9) = multiply(sk_c6,multiply(sk_c3,X9))
| ~ spl3_2 ),
inference(superposition,[],[f3,f106]) ).
fof(f106,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl3_2 ),
inference(superposition,[],[f2,f35]) ).
fof(f105,plain,
( spl3_11
| spl3_12 ),
inference(avatar_split_clause,[],[f15,f78,f73]) ).
fof(f15,axiom,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f103,plain,
( spl3_2
| spl3_7 ),
inference(avatar_split_clause,[],[f10,f54,f33]) ).
fof(f10,axiom,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f102,plain,
( spl3_11
| spl3_9 ),
inference(avatar_split_clause,[],[f19,f63,f73]) ).
fof(f19,axiom,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f101,plain,
( spl3_14
| spl3_15 ),
inference(avatar_split_clause,[],[f22,f99,f91]) ).
fof(f91,plain,
( spl3_14
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f22,plain,
! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sP0
| sk_c7 != inverse(X3) ),
inference(cnf_transformation,[],[f22_D]) ).
fof(f22_D,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3) )
<=> ~ sP0 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f97,plain,
( spl3_1
| spl3_10 ),
inference(avatar_split_clause,[],[f5,f68,f29]) ).
fof(f5,axiom,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f96,plain,
( spl3_9
| spl3_8 ),
inference(avatar_split_clause,[],[f20,f58,f63]) ).
fof(f20,axiom,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f95,plain,
( spl3_8
| spl3_12 ),
inference(avatar_split_clause,[],[f16,f78,f58]) ).
fof(f16,axiom,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f94,plain,
( ~ spl3_4
| spl3_13
| ~ spl3_14
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f86,f46,f91,f88,f41]) ).
fof(f41,plain,
( spl3_4
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f46,plain,
( spl3_5
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f86,plain,
! [X5] :
( ~ sP1
| ~ sP0
| sk_c6 != inverse(X5)
| ~ sP2
| sk_c7 != multiply(X5,sk_c6) ),
inference(trivial_inequality_removal,[],[f85]) ).
fof(f85,plain,
! [X5] :
( sk_c7 != multiply(X5,sk_c6)
| sk_c6 != inverse(X5)
| sk_c5 != sk_c5
| ~ sP0
| ~ sP2
| ~ sP1 ),
inference(forward_demodulation,[],[f27,f4]) ).
fof(f27,plain,
! [X5] :
( sk_c7 != multiply(X5,sk_c6)
| ~ sP2
| multiply(sk_c6,sk_c7) != sk_c5
| ~ sP0
| sk_c6 != inverse(X5)
| ~ sP1 ),
inference(general_splitting,[],[f25,f26_D]) ).
fof(f26,plain,
! [X4] :
( sP2
| sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4) ),
inference(cnf_transformation,[],[f26_D]) ).
fof(f26_D,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4) )
<=> ~ sP2 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f25,plain,
! [X4,X5] :
( multiply(sk_c6,sk_c7) != sk_c5
| sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4)
| sk_c6 != inverse(X5)
| sk_c7 != multiply(X5,sk_c6)
| ~ sP0
| ~ sP1 ),
inference(general_splitting,[],[f23,f24_D]) ).
fof(f24,plain,
! [X6] :
( sk_c5 != multiply(X6,sk_c6)
| sk_c5 != inverse(X6)
| sP1 ),
inference(cnf_transformation,[],[f24_D]) ).
fof(f24_D,plain,
( ! [X6] :
( sk_c5 != multiply(X6,sk_c6)
| sk_c5 != inverse(X6) )
<=> ~ sP1 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP1])]) ).
fof(f23,plain,
! [X6,X4,X5] :
( multiply(sk_c6,sk_c7) != sk_c5
| sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4)
| sk_c5 != multiply(X6,sk_c6)
| sk_c6 != inverse(X5)
| sk_c5 != inverse(X6)
| sk_c7 != multiply(X5,sk_c6)
| ~ sP0 ),
inference(general_splitting,[],[f21,f22_D]) ).
fof(f21,axiom,
! [X3,X6,X4,X5] :
( sk_c7 != multiply(X3,sk_c6)
| sk_c7 != inverse(X3)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c6 != multiply(X4,sk_c5)
| sk_c6 != inverse(X4)
| sk_c5 != multiply(X6,sk_c6)
| sk_c6 != inverse(X5)
| sk_c5 != inverse(X6)
| sk_c7 != multiply(X5,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f84,plain,
( spl3_7
| spl3_10 ),
inference(avatar_split_clause,[],[f9,f68,f54]) ).
fof(f9,axiom,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f83,plain,
( spl3_12
| spl3_10 ),
inference(avatar_split_clause,[],[f13,f68,f78]) ).
fof(f13,axiom,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f81,plain,
( spl3_12
| spl3_2 ),
inference(avatar_split_clause,[],[f14,f33,f78]) ).
fof(f14,axiom,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f71,plain,
( spl3_10
| spl3_9 ),
inference(avatar_split_clause,[],[f17,f63,f68]) ).
fof(f17,axiom,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f66,plain,
( spl3_2
| spl3_9 ),
inference(avatar_split_clause,[],[f18,f63,f33]) ).
fof(f18,axiom,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f52,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f24,f50,f46]) ).
fof(f44,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f26,f41,f38]) ).
fof(f36,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f6,f33,f29]) ).
fof(f6,axiom,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP344-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 29 22:17:44 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.49 % (1434)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.50 % (1433)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50 % (1426)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.50 % (1424)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.51 % (1435)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)
% 0.21/0.51 % (1431)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51 % (1428)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 TRYING [1]
% 0.21/0.51 % (1450)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.51 TRYING [2]
% 0.21/0.51 TRYING [3]
% 0.21/0.51 % (1438)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.52 % (1446)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.52 % (1432)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.52 % (1441)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.52 % (1430)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52 % (1432)Instruction limit reached!
% 0.21/0.52 % (1432)------------------------------
% 0.21/0.52 % (1432)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (1434)First to succeed.
% 0.21/0.52 % (1445)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.52 % (1442)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.52 % (1427)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53 TRYING [4]
% 0.21/0.53 TRYING [1]
% 0.21/0.53 TRYING [2]
% 0.21/0.53 % (1440)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.53 % (1432)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53 % (1432)Termination reason: Unknown
% 0.21/0.53 % (1432)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (1432)Memory used [KB]: 5373
% 0.21/0.53 % (1432)Time elapsed: 0.115 s
% 0.21/0.53 % (1432)Instructions burned: 2 (million)
% 0.21/0.53 % (1432)------------------------------
% 0.21/0.53 % (1432)------------------------------
% 0.21/0.53 % (1449)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.53 TRYING [1]
% 0.21/0.53 % (1444)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.53 TRYING [2]
% 1.37/0.53 % (1434)Refutation found. Thanks to Tanya!
% 1.37/0.53 % SZS status Unsatisfiable for theBenchmark
% 1.37/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.37/0.53 % (1434)------------------------------
% 1.37/0.53 % (1434)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.53 % (1434)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.53 % (1434)Termination reason: Refutation
% 1.37/0.53
% 1.37/0.53 % (1434)Memory used [KB]: 5756
% 1.37/0.53 % (1434)Time elapsed: 0.125 s
% 1.37/0.53 % (1434)Instructions burned: 17 (million)
% 1.37/0.53 % (1434)------------------------------
% 1.37/0.53 % (1434)------------------------------
% 1.37/0.53 % (1423)Success in time 0.181 s
%------------------------------------------------------------------------------