TSTP Solution File: SET843-2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : n015.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 18:25:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 15 unt; 0 def)
% Number of atoms : 167 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 179 ( 87 ~; 89 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f213,plain,
$false,
inference(avatar_sat_refutation,[],[f27,f28,f154,f198,f210]) ).
fof(f210,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f209,f20,f24]) ).
fof(f24,plain,
( spl5_2
<=> v_m = sF3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f20,plain,
( spl5_1
<=> v_m = sF4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f209,plain,
( v_m = sF3
| ~ spl5_1 ),
inference(forward_demodulation,[],[f208,f21]) ).
fof(f21,plain,
( v_m = sF4
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f208,plain,
( sF4 = sF3
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f207,f38]) ).
fof(f38,plain,
c_lessequals(v_m,sF3,sF2),
inference(superposition,[],[f37,f15]) ).
fof(f15,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = sF3,
introduced(function_definition,[]) ).
fof(f37,plain,
! [X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,t_a),sF2),
inference(forward_demodulation,[],[f32,f13]) ).
fof(f13,plain,
sF2 = tc_set(sF1),
introduced(function_definition,[]) ).
fof(f32,plain,
! [X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,t_a),tc_set(sF1)),
inference(superposition,[],[f4,f12]) ).
fof(f12,plain,
tc_set(t_a) = sF1,
introduced(function_definition,[]) ).
fof(f4,axiom,
! [X2,X3,X4] : c_lessequals(X3,c_Zorn_Osucc(X4,X3,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f207,plain,
( sF4 = sF3
| ~ c_lessequals(v_m,sF3,sF2)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f132,f21]) ).
fof(f132,plain,
( ~ c_lessequals(sF4,sF3,sF2)
| sF4 = sF3 ),
inference(subsumption_resolution,[],[f131,f14]) ).
fof(f14,plain,
c_in(v_m,sF0,sF2),
inference(definition_folding,[],[f8,f13,f12,f11]) ).
fof(f11,plain,
c_Zorn_OTFin(v_S,t_a) = sF0,
introduced(function_definition,[]) ).
fof(f8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f131,plain,
( ~ c_lessequals(sF4,sF3,sF2)
| ~ c_in(v_m,sF0,sF2)
| sF4 = sF3 ),
inference(superposition,[],[f120,f15]) ).
fof(f120,plain,
! [X0] :
( ~ c_lessequals(sF4,c_Zorn_Osucc(v_S,X0,t_a),sF2)
| ~ c_in(X0,sF0,sF2)
| sF4 = c_Zorn_Osucc(v_S,X0,t_a) ),
inference(resolution,[],[f106,f52]) ).
fof(f52,plain,
! [X2,X3] :
( ~ c_lessequals(X3,X2,sF2)
| X2 = X3
| ~ c_lessequals(X2,X3,sF2) ),
inference(superposition,[],[f2,f13]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f106,plain,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),sF4,sF2)
| ~ c_in(X0,sF0,sF2) ),
inference(resolution,[],[f102,f44]) ).
fof(f44,plain,
! [X0] :
( ~ c_in(X0,sF0,sF2)
| c_lessequals(X0,sF4,sF2) ),
inference(forward_demodulation,[],[f43,f13]) ).
fof(f43,plain,
! [X0] :
( c_lessequals(X0,sF4,tc_set(sF1))
| ~ c_in(X0,sF0,sF2) ),
inference(forward_demodulation,[],[f40,f13]) ).
fof(f40,plain,
! [X0] :
( ~ c_in(X0,sF0,tc_set(sF1))
| c_lessequals(X0,sF4,tc_set(sF1)) ),
inference(superposition,[],[f1,f16]) ).
fof(f16,plain,
sF4 = c_Union(sF0,sF1),
introduced(function_definition,[]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
fof(f102,plain,
! [X0] :
( c_in(c_Zorn_Osucc(v_S,X0,t_a),sF0,sF2)
| ~ c_in(X0,sF0,sF2) ),
inference(forward_demodulation,[],[f101,f13]) ).
fof(f101,plain,
! [X0] :
( ~ c_in(X0,sF0,sF2)
| c_in(c_Zorn_Osucc(v_S,X0,t_a),sF0,tc_set(sF1)) ),
inference(forward_demodulation,[],[f100,f12]) ).
fof(f100,plain,
! [X0] :
( ~ c_in(X0,sF0,sF2)
| c_in(c_Zorn_Osucc(v_S,X0,t_a),sF0,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f99,f13]) ).
fof(f99,plain,
! [X0] :
( ~ c_in(X0,sF0,tc_set(sF1))
| c_in(c_Zorn_Osucc(v_S,X0,t_a),sF0,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f88,f12]) ).
fof(f88,plain,
! [X0] :
( ~ c_in(X0,sF0,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Osucc(v_S,X0,t_a),sF0,tc_set(tc_set(t_a))) ),
inference(superposition,[],[f5,f11]) ).
fof(f5,axiom,
! [X2,X3,X4] :
( c_in(c_Zorn_Osucc(X4,X3,X2),c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
fof(f198,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f197,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f196,f59]) ).
fof(f59,plain,
( ~ c_lessequals(sF4,v_m,sF2)
| spl5_1 ),
inference(subsumption_resolution,[],[f58,f22]) ).
fof(f22,plain,
( v_m != sF4
| spl5_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f58,plain,
( v_m = sF4
| ~ c_lessequals(sF4,v_m,sF2) ),
inference(resolution,[],[f52,f45]) ).
fof(f45,plain,
c_lessequals(v_m,sF4,sF2),
inference(resolution,[],[f44,f14]) ).
fof(f196,plain,
( c_lessequals(sF4,v_m,sF2)
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f192,f112]) ).
fof(f112,plain,
( c_in(sF4,sF0,sF2)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f111,plain,
( spl5_3
<=> c_in(sF4,sF0,sF2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f192,plain,
( ! [X0] :
( ~ c_in(X0,sF0,sF2)
| c_lessequals(X0,v_m,sF2) )
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f191,f14]) ).
fof(f191,plain,
( ! [X0] :
( ~ c_in(X0,sF0,sF2)
| c_lessequals(X0,v_m,sF2)
| ~ c_in(v_m,sF0,sF2) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f190,f11]) ).
fof(f190,plain,
( ! [X0] :
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),sF2)
| ~ c_in(X0,sF0,sF2)
| c_lessequals(X0,v_m,sF2) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f189,f13]) ).
fof(f189,plain,
( ! [X0] :
( ~ c_in(X0,sF0,sF2)
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(sF1))
| c_lessequals(X0,v_m,sF2) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f188,f12]) ).
fof(f188,plain,
( ! [X0] :
( ~ c_in(X0,sF0,sF2)
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,sF2) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f187,f13]) ).
fof(f187,plain,
( ! [X0] :
( c_lessequals(X0,v_m,tc_set(sF1))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,sF0,sF2) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f186,f12]) ).
fof(f186,plain,
( ! [X0] :
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,sF0,sF2)
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f185,f11]) ).
fof(f185,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),sF2)
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f184,f13]) ).
fof(f184,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(sF1))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f183,f12]) ).
fof(f183,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f171,f25]) ).
fof(f25,plain,
( v_m = sF3
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f171,plain,
! [X0] :
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m != sF3 ),
inference(superposition,[],[f7,f15]) ).
fof(f7,axiom,
! [X2,X6,X7,X4] :
( c_Zorn_Osucc(X4,X6,X2) != X6
| ~ c_in(X7,c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2)))
| c_lessequals(X7,X6,tc_set(tc_set(X2)))
| ~ c_in(X6,c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
fof(f154,plain,
spl5_3,
inference(avatar_contradiction_clause,[],[f153]) ).
fof(f153,plain,
( $false
| spl5_3 ),
inference(subsumption_resolution,[],[f152,f3]) ).
fof(f3,axiom,
! [X2,X1] : c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f152,plain,
( ~ c_lessequals(sF0,sF0,tc_set(sF2))
| spl5_3 ),
inference(subsumption_resolution,[],[f151,f113]) ).
fof(f113,plain,
( ~ c_in(sF4,sF0,sF2)
| spl5_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f151,plain,
( ~ c_lessequals(sF0,sF0,tc_set(sF2))
| c_in(sF4,sF0,sF2) ),
inference(superposition,[],[f146,f16]) ).
fof(f146,plain,
! [X0] :
( c_in(c_Union(X0,sF1),sF0,sF2)
| ~ c_lessequals(X0,sF0,tc_set(sF2)) ),
inference(forward_demodulation,[],[f145,f13]) ).
fof(f145,plain,
! [X0] :
( ~ c_lessequals(X0,sF0,tc_set(sF2))
| c_in(c_Union(X0,sF1),sF0,tc_set(sF1)) ),
inference(forward_demodulation,[],[f144,f12]) ).
fof(f144,plain,
! [X0] :
( ~ c_lessequals(X0,sF0,tc_set(sF2))
| c_in(c_Union(X0,tc_set(t_a)),sF0,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f143,f13]) ).
fof(f143,plain,
! [X0] :
( ~ c_lessequals(X0,sF0,tc_set(tc_set(sF1)))
| c_in(c_Union(X0,tc_set(t_a)),sF0,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f140,f12]) ).
fof(f140,plain,
! [X0] :
( ~ c_lessequals(X0,sF0,tc_set(tc_set(tc_set(t_a))))
| c_in(c_Union(X0,tc_set(t_a)),sF0,tc_set(tc_set(t_a))) ),
inference(superposition,[],[f6,f11]) ).
fof(f6,axiom,
! [X2,X4,X5] :
( c_in(c_Union(X5,tc_set(X2)),c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X5,c_Zorn_OTFin(X4,X2),tc_set(tc_set(tc_set(X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f28,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f17,f24,f20]) ).
fof(f17,plain,
( v_m = sF3
| v_m = sF4 ),
inference(definition_folding,[],[f10,f16,f12,f11,f15]) ).
fof(f10,axiom,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f27,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f18,f24,f20]) ).
fof(f18,plain,
( v_m != sF3
| v_m != sF4 ),
inference(definition_folding,[],[f9,f16,f12,f11,f15]) ).
fof(f9,axiom,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % 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 : n015.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 : Tue Aug 30 14:35:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.48 % (6428)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.49 % (6436)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.49 % (6436)First to succeed.
% 0.20/0.49 TRYING [1]
% 0.20/0.49 TRYING [2]
% 0.20/0.50 TRYING [3]
% 0.20/0.50 % (6436)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (6436)------------------------------
% 0.20/0.50 % (6436)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (6436)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (6436)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (6436)Memory used [KB]: 5500
% 0.20/0.50 % (6436)Time elapsed: 0.078 s
% 0.20/0.50 % (6436)Instructions burned: 6 (million)
% 0.20/0.50 % (6436)------------------------------
% 0.20/0.50 % (6436)------------------------------
% 0.20/0.50 % (6410)Success in time 0.149 s
%------------------------------------------------------------------------------