TSTP Solution File: ALG179+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ALG179+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : n009.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 15:43:22 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 12 unt; 0 def)
% Number of atoms : 211 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 235 ( 86 ~; 74 |; 37 &)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f638,plain,
$false,
inference(avatar_sat_refutation,[],[f115,f119,f633,f637]) ).
fof(f637,plain,
spl2_10,
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f636,plain,
( $false
| spl2_10 ),
inference(subsumption_resolution,[],[f635,f27]) ).
fof(f27,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( sorti2(sK0)
& sorti2(sK1)
& sK0 != op2(op2(sK0,sK1),sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f16,f15]) ).
fof(f15,plain,
( ? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(op2(X0,X1),X1) != X0 ) )
=> ( sorti2(sK0)
& ? [X1] :
( sorti2(X1)
& op2(op2(sK0,X1),X1) != sK0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X1] :
( sorti2(X1)
& op2(op2(sK0,X1),X1) != sK0 )
=> ( sorti2(sK1)
& sK0 != op2(op2(sK0,sK1),sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(op2(X0,X1),X1) != X0 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(op2(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f635,plain,
( ~ sorti2(sK1)
| spl2_10 ),
inference(resolution,[],[f237,f22]) ).
fof(f22,plain,
! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X2] :
( h(j(X2)) = X2
| ~ sorti2(X2) )
& ! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( op2(h(X3),h(X4)) = h(op1(X3,X4))
| ~ sorti1(X4) ) )
& ! [X5] :
( ~ sorti1(X5)
| sorti2(h(X5)) )
& ! [X6] :
( ~ sorti2(X6)
| ! [X7] :
( ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
( ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) )
& ! [X2] :
( h(j(X2)) = X2
| ~ sorti2(X2) )
& ! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( op2(h(X3),h(X4)) = h(op1(X3,X4))
| ~ sorti1(X4) ) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X6] :
( ~ sorti2(X6)
| ! [X7] :
( ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) ) ) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
( ! [X6] :
( ~ sorti2(X6)
| ! [X7] :
( ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) ) )
& ! [X3] :
( ~ sorti1(X3)
| ! [X4] :
( op2(h(X3),h(X4)) = h(op1(X3,X4))
| ~ sorti1(X4) ) )
& ! [X2] :
( h(j(X2)) = X2
| ~ sorti2(X2) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X0] :
( ~ sorti1(X0)
| sorti2(h(X0)) )
& ! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> ! [X7] :
( sorti2(X7)
=> j(op2(X6,X7)) = op1(j(X6),j(X7)) ) )
& ! [X3] :
( sorti1(X3)
=> ! [X4] :
( sorti1(X4)
=> op2(h(X3),h(X4)) = h(op1(X3,X4)) ) )
& ! [X2] :
( sorti2(X2)
=> h(j(X2)) = X2 )
& ! [X5] :
( sorti1(X5)
=> j(h(X5)) = X5 ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f237,plain,
( ~ sorti1(j(sK1))
| spl2_10 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl2_10
<=> sorti1(j(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f633,plain,
( ~ spl2_3
| ~ spl2_10 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f632,plain,
( $false
| ~ spl2_3
| ~ spl2_10 ),
inference(subsumption_resolution,[],[f631,f26]) ).
fof(f26,plain,
sK0 != op2(op2(sK0,sK1),sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f631,plain,
( sK0 = op2(op2(sK0,sK1),sK1)
| ~ spl2_3
| ~ spl2_10 ),
inference(forward_demodulation,[],[f630,f31]) ).
fof(f31,plain,
sK0 = h(j(sK0)),
inference(resolution,[],[f21,f28]) ).
fof(f28,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f21,plain,
! [X2] :
( ~ sorti2(X2)
| h(j(X2)) = X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f630,plain,
( op2(op2(sK0,sK1),sK1) = h(j(sK0))
| ~ spl2_3
| ~ spl2_10 ),
inference(forward_demodulation,[],[f629,f405]) ).
fof(f405,plain,
j(sK0) = op1(j(op2(sK0,sK1)),j(sK1)),
inference(forward_demodulation,[],[f403,f217]) ).
fof(f217,plain,
op1(j(sK0),j(sK1)) = j(op2(sK0,sK1)),
inference(resolution,[],[f184,f27]) ).
fof(f184,plain,
! [X9] :
( ~ sorti2(X9)
| j(op2(sK0,X9)) = op1(j(sK0),j(X9)) ),
inference(resolution,[],[f18,f28]) ).
fof(f18,plain,
! [X6,X7] :
( ~ sorti2(X6)
| ~ sorti2(X7)
| j(op2(X6,X7)) = op1(j(X6),j(X7)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f403,plain,
j(sK0) = op1(op1(j(sK0),j(sK1)),j(sK1)),
inference(resolution,[],[f290,f27]) ).
fof(f290,plain,
! [X0] :
( ~ sorti2(X0)
| j(sK0) = op1(op1(j(sK0),j(X0)),j(X0)) ),
inference(resolution,[],[f282,f22]) ).
fof(f282,plain,
! [X9] :
( ~ sorti1(X9)
| j(sK0) = op1(op1(j(sK0),X9),X9) ),
inference(resolution,[],[f44,f28]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti1(X0)
| j(X1) = op1(op1(j(X1),X0),X0) ),
inference(resolution,[],[f24,f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(op1(X0,X1),X1) = X0 ),
inference(cnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( op1(op1(X0,X1),X1) = X0
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(op1(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f629,plain,
( h(op1(j(op2(sK0,sK1)),j(sK1))) = op2(op2(sK0,sK1),sK1)
| ~ spl2_3
| ~ spl2_10 ),
inference(forward_demodulation,[],[f615,f71]) ).
fof(f71,plain,
h(j(op2(sK0,sK1))) = op2(sK0,sK1),
inference(resolution,[],[f62,f27]) ).
fof(f62,plain,
! [X5] :
( ~ sorti2(X5)
| op2(sK0,X5) = h(j(op2(sK0,X5))) ),
inference(resolution,[],[f37,f28]) ).
fof(f37,plain,
! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f29,f21]) ).
fof(f29,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ! [X1] :
( ~ sorti2(X1)
| sorti2(op2(X0,X1)) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f615,plain,
( h(op1(j(op2(sK0,sK1)),j(sK1))) = op2(h(j(op2(sK0,sK1))),sK1)
| ~ spl2_3
| ~ spl2_10 ),
inference(resolution,[],[f558,f107]) ).
fof(f107,plain,
( sorti1(j(op2(sK0,sK1)))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f106,plain,
( spl2_3
<=> sorti1(j(op2(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f558,plain,
( ! [X7] :
( ~ sorti1(X7)
| h(op1(X7,j(sK1))) = op2(h(X7),sK1) )
| ~ spl2_10 ),
inference(forward_demodulation,[],[f537,f30]) ).
fof(f30,plain,
sK1 = h(j(sK1)),
inference(resolution,[],[f21,f27]) ).
fof(f537,plain,
( ! [X7] :
( ~ sorti1(X7)
| h(op1(X7,j(sK1))) = op2(h(X7),h(j(sK1))) )
| ~ spl2_10 ),
inference(resolution,[],[f20,f236]) ).
fof(f236,plain,
( sorti1(j(sK1))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f20,plain,
! [X3,X4] :
( ~ sorti1(X4)
| ~ sorti1(X3)
| op2(h(X3),h(X4)) = h(op1(X3,X4)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f119,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f118,plain,
( $false
| spl2_4 ),
inference(subsumption_resolution,[],[f117,f28]) ).
fof(f117,plain,
( ~ sorti2(sK0)
| spl2_4 ),
inference(subsumption_resolution,[],[f116,f27]) ).
fof(f116,plain,
( ~ sorti2(sK1)
| ~ sorti2(sK0)
| spl2_4 ),
inference(resolution,[],[f111,f29]) ).
fof(f111,plain,
( ~ sorti2(op2(sK0,sK1))
| spl2_4 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f110,plain,
( spl2_4
<=> sorti2(op2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f115,plain,
( ~ spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f114,f106,f110]) ).
fof(f114,plain,
( ~ sorti2(op2(sK0,sK1))
| spl2_3 ),
inference(resolution,[],[f108,f22]) ).
fof(f108,plain,
( ~ sorti1(j(op2(sK0,sK1)))
| spl2_3 ),
inference(avatar_component_clause,[],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG179+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 14:55:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.44 % (30565)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.46 % (30561)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)
% 0.20/0.47 % (30561)Refutation not found, incomplete strategy% (30561)------------------------------
% 0.20/0.47 % (30561)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47 % (30561)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47 % (30561)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.47
% 0.20/0.47 % (30561)Memory used [KB]: 5373
% 0.20/0.47 % (30561)Time elapsed: 0.094 s
% 0.20/0.47 % (30561)Instructions burned: 2 (million)
% 0.20/0.47 % (30561)------------------------------
% 0.20/0.47 % (30561)------------------------------
% 0.20/0.47 % (30580)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)
% 0.20/0.48 % (30573)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48 % (30565)First to succeed.
% 0.20/0.49 % (30575)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.49 % (30577)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.49 % (30565)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (30565)------------------------------
% 0.20/0.49 % (30565)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (30565)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (30565)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (30565)Memory used [KB]: 5756
% 0.20/0.49 % (30565)Time elapsed: 0.095 s
% 0.20/0.49 % (30565)Instructions burned: 25 (million)
% 0.20/0.49 % (30565)------------------------------
% 0.20/0.49 % (30565)------------------------------
% 0.20/0.49 % (30559)Success in time 0.149 s
%------------------------------------------------------------------------------