TSTP Solution File: GRP040-4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n012.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 16:13:48 EDT 2022
% Result : Unsatisfiable 1.33s 0.52s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 29
% Syntax : Number of formulae : 84 ( 26 unt; 0 def)
% Number of atoms : 173 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 170 ( 81 ~; 79 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f558,plain,
$false,
inference(avatar_sat_refutation,[],[f106,f110,f185,f192,f194,f446,f451,f467,f546,f553,f557]) ).
fof(f557,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f556,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f176,f18]) ).
fof(f18,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
fof(f176,plain,
( subgroup_member(d)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f174,plain,
( spl0_6
<=> subgroup_member(d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f553,plain,
( ~ spl0_9
| spl0_26 ),
inference(avatar_split_clause,[],[f548,f537,f189]) ).
fof(f189,plain,
( spl0_9
<=> subgroup_member(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f537,plain,
( spl0_26
<=> subgroup_member(inverse(c)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f548,plain,
( ~ subgroup_member(c)
| spl0_26 ),
inference(resolution,[],[f539,f11]) ).
fof(f11,axiom,
! [X6] :
( subgroup_member(inverse(X6))
| ~ subgroup_member(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f539,plain,
( ~ subgroup_member(inverse(c))
| spl0_26 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f546,plain,
( ~ spl0_26
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f526,f440,f537]) ).
fof(f440,plain,
( spl0_20
<=> ! [X4] :
( ~ product(X4,b,a)
| ~ subgroup_member(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f526,plain,
( ~ subgroup_member(inverse(c))
| ~ spl0_20 ),
inference(resolution,[],[f525,f441]) ).
fof(f441,plain,
( ! [X4] :
( ~ product(X4,b,a)
| ~ subgroup_member(X4) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f525,plain,
product(inverse(c),b,a),
inference(superposition,[],[f5,f509]) ).
fof(f509,plain,
a = multiply(inverse(c),b),
inference(resolution,[],[f505,f163]) ).
fof(f163,plain,
! [X12,X13] :
( ~ product(inverse(X12),X13,identity)
| X12 = X13 ),
inference(resolution,[],[f12,f3]) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f12,axiom,
! [X8,X6,X9,X7] :
( ~ product(X6,X7,X8)
| X7 = X9
| ~ product(X6,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f505,plain,
product(inverse(a),multiply(inverse(c),b),identity),
inference(forward_demodulation,[],[f504,f21]) ).
fof(f21,axiom,
! [X6] : inverse(inverse(X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
fof(f504,plain,
product(inverse(a),multiply(inverse(c),inverse(inverse(b))),identity),
inference(resolution,[],[f495,f252]) ).
fof(f252,plain,
! [X2,X3,X4] :
( ~ product(X2,X3,X4)
| product(X2,multiply(X3,inverse(X4)),identity) ),
inference(resolution,[],[f245,f5]) ).
fof(f245,plain,
! [X10,X11,X9,X12] :
( ~ product(X11,inverse(X12),X10)
| product(X9,X10,identity)
| ~ product(X9,X11,X12) ),
inference(resolution,[],[f7,f22]) ).
fof(f22,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(superposition,[],[f3,f21]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X2,X3)
| product(X0,X5,X3)
| ~ product(X0,X1,X4)
| ~ product(X1,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f495,plain,
product(inverse(a),inverse(c),inverse(b)),
inference(superposition,[],[f5,f413]) ).
fof(f413,plain,
inverse(b) = multiply(inverse(a),inverse(c)),
inference(resolution,[],[f275,f160]) ).
fof(f160,plain,
! [X6,X5] :
( ~ product(X5,X6,identity)
| inverse(X5) = X6 ),
inference(resolution,[],[f12,f22]) ).
fof(f275,plain,
product(b,multiply(inverse(a),inverse(c)),identity),
inference(resolution,[],[f252,f19]) ).
fof(f19,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f467,plain,
spl0_22,
inference(avatar_contradiction_clause,[],[f464]) ).
fof(f464,plain,
( $false
| spl0_22 ),
inference(resolution,[],[f450,f17]) ).
fof(f17,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f450,plain,
( ~ subgroup_member(b)
| spl0_22 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f448,plain,
( spl0_22
<=> subgroup_member(b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f451,plain,
( ~ spl0_22
| spl0_21 ),
inference(avatar_split_clause,[],[f427,f443,f448]) ).
fof(f443,plain,
( spl0_21
<=> subgroup_member(multiply(inverse(a),inverse(c))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f427,plain,
( subgroup_member(multiply(inverse(a),inverse(c)))
| ~ subgroup_member(b) ),
inference(superposition,[],[f24,f412]) ).
fof(f412,plain,
b = inverse(multiply(inverse(a),inverse(c))),
inference(resolution,[],[f275,f231]) ).
fof(f231,plain,
! [X0,X1] :
( ~ product(X1,X0,identity)
| inverse(X0) = X1 ),
inference(superposition,[],[f223,f21]) ).
fof(f223,plain,
! [X6,X5] :
( ~ product(X6,inverse(X5),identity)
| X5 = X6 ),
inference(resolution,[],[f13,f22]) ).
fof(f13,axiom,
! [X8,X6,X9,X7] :
( ~ product(X6,X7,X8)
| X6 = X9
| ~ product(X9,X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f24,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(superposition,[],[f11,f21]) ).
fof(f446,plain,
( spl0_20
| ~ spl0_21
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f434,f104,f443,f440]) ).
fof(f104,plain,
( spl0_2
<=> ! [X2] :
( ~ subgroup_member(X2)
| ~ product(X2,identity,inverse(a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f434,plain,
( ! [X4] :
( ~ subgroup_member(multiply(inverse(a),inverse(c)))
| ~ product(X4,b,a)
| ~ subgroup_member(X4) )
| ~ spl0_2 ),
inference(superposition,[],[f116,f412]) ).
fof(f116,plain,
( ! [X0,X1] :
( ~ product(X1,inverse(X0),a)
| ~ subgroup_member(X0)
| ~ subgroup_member(X1) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f114,f21]) ).
fof(f114,plain,
( ! [X0,X1] :
( ~ product(X1,inverse(X0),inverse(inverse(a)))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) )
| ~ spl0_2 ),
inference(resolution,[],[f112,f91]) ).
fof(f91,plain,
! [X6,X4,X5] :
( subgroup_member(X6)
| ~ subgroup_member(X4)
| ~ product(X5,inverse(X4),inverse(X6))
| ~ subgroup_member(X5) ),
inference(resolution,[],[f9,f24]) ).
fof(f9,axiom,
! [X8,X6,X7] :
( subgroup_member(X8)
| ~ subgroup_member(X7)
| ~ product(X6,inverse(X7),X8)
| ~ subgroup_member(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
fof(f112,plain,
( ~ subgroup_member(inverse(a))
| ~ spl0_2 ),
inference(resolution,[],[f105,f2]) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f105,plain,
( ! [X2] :
( ~ product(X2,identity,inverse(a))
| ~ subgroup_member(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f194,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| ~ spl0_8 ),
inference(resolution,[],[f184,f16]) ).
fof(f16,axiom,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
fof(f184,plain,
( subgroup_member(a)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f182,plain,
( spl0_8
<=> subgroup_member(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f192,plain,
( spl0_6
| spl0_9
| spl0_8
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f187,f178,f182,f189,f174]) ).
fof(f178,plain,
( spl0_7
<=> c = element_in_O2(a,d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f187,plain,
( subgroup_member(a)
| subgroup_member(c)
| subgroup_member(d)
| ~ spl0_7 ),
inference(superposition,[],[f14,f180]) ).
fof(f180,plain,
( c = element_in_O2(a,d)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f14,axiom,
! [X6,X7] :
( subgroup_member(element_in_O2(X6,X7))
| subgroup_member(X7)
| subgroup_member(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f185,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f172,f182,f178,f174]) ).
fof(f172,plain,
( subgroup_member(a)
| c = element_in_O2(a,d)
| subgroup_member(d) ),
inference(resolution,[],[f164,f15]) ).
fof(f15,axiom,
! [X6,X7] :
( product(X6,element_in_O2(X6,X7),X7)
| subgroup_member(X6)
| subgroup_member(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f164,plain,
! [X14] :
( ~ product(a,X14,d)
| c = X14 ),
inference(resolution,[],[f12,f20]) ).
fof(f20,axiom,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f110,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f107,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f102,f10]) ).
fof(f10,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
fof(f102,plain,
( ~ subgroup_member(identity)
| spl0_1 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f100,plain,
( spl0_1
<=> subgroup_member(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f106,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f98,f104,f100]) ).
fof(f98,plain,
! [X2] :
( ~ subgroup_member(X2)
| ~ product(X2,identity,inverse(a))
| ~ subgroup_member(identity) ),
inference(superposition,[],[f92,f37]) ).
fof(f37,plain,
identity = inverse(identity),
inference(resolution,[],[f29,f1]) ).
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f29,plain,
! [X6,X5] :
( ~ product(X6,inverse(X6),X5)
| identity = X5 ),
inference(resolution,[],[f6,f22]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| X2 = X3
| ~ product(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f92,plain,
! [X0,X1] :
( ~ product(X1,inverse(X0),inverse(a))
| ~ subgroup_member(X0)
| ~ subgroup_member(X1) ),
inference(resolution,[],[f91,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n012.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 22:09:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (30944)dis+1011_1:16_fsr=off:nwc=2.0:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.49 % (30952)lrs+30_1:12_av=off:bs=unit_only:fsd=on:gs=on:lwlo=on:newcnf=on:slsq=on:slsqr=1,2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (30938)lrs+10_1:1_kws=precedence:lwlo=on:tgt=ground:i=99966:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99966Mi)
% 0.19/0.50 % (30947)lrs+1011_1:1_atotf=0.0306256:ep=RST:mep=off:nm=0:sos=all:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50 % (30960)lrs+1010_1:1_bd=off:fsr=off:sd=1:sos=on:ss=axioms:i=67:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/67Mi)
% 0.19/0.51 % (30942)lrs+10_1:1_bd=off:drc=off:lcm=reverse:nwc=5.0:sd=1:sgt=16:spb=goal_then_units:ss=axioms:to=lpo:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 0.19/0.51 % (30952)Instruction limit reached!
% 0.19/0.51 % (30952)------------------------------
% 0.19/0.51 % (30952)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (30952)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (30952)Termination reason: Unknown
% 0.19/0.51 % (30952)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (30952)Memory used [KB]: 5884
% 0.19/0.51 % (30952)Time elapsed: 0.121 s
% 0.19/0.51 % (30952)Instructions burned: 3 (million)
% 0.19/0.51 % (30952)------------------------------
% 0.19/0.51 % (30952)------------------------------
% 0.19/0.51 % (30963)dis+10_1:1_add=large:alpa=false:anc=none:fd=off:lcm=reverse:nwc=5.0:sd=2:sgt=20:ss=included:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.19/0.51 % (30944)First to succeed.
% 0.19/0.52 % (30954)fmb+10_1:1_fmbes=contour:fmbsr=2.0:fmbsso=input_usage:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.52 % (30945)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.52 TRYING [1]
% 0.19/0.52 TRYING [2]
% 1.33/0.52 % (30944)Refutation found. Thanks to Tanya!
% 1.33/0.52 % SZS status Unsatisfiable for theBenchmark
% 1.33/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.52 % (30944)------------------------------
% 1.33/0.52 % (30944)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.52 % (30944)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.52 % (30944)Termination reason: Refutation
% 1.33/0.52
% 1.33/0.52 % (30944)Memory used [KB]: 6140
% 1.33/0.52 % (30944)Time elapsed: 0.108 s
% 1.33/0.52 % (30944)Instructions burned: 18 (million)
% 1.33/0.52 % (30944)------------------------------
% 1.33/0.52 % (30944)------------------------------
% 1.33/0.52 % (30935)Success in time 0.168 s
%------------------------------------------------------------------------------