TSTP Solution File: SET853-2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET853-2 : 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 : n002.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 18:25:54 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 139 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 60 ~; 79 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[f24,f41,f60,f88,f93,f109,f110,f111,f134,f139,f147]) ).
fof(f147,plain,
( spl0_5
| ~ spl0_4
| spl0_1
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f145,f132,f17,f34,f38]) ).
fof(f38,plain,
( spl0_5
<=> c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f34,plain,
( spl0_4
<=> c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f17,plain,
( spl0_1
<=> c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f132,plain,
( spl0_14
<=> ! [X0] :
( c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f145,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| spl0_1
| ~ spl0_14 ),
inference(resolution,[],[f133,f19]) ).
fof(f19,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f133,plain,
( ! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a))) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f139,plain,
( ~ spl0_7
| spl0_13
| spl0_5
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f136,f17,f34,f38,f128,f57]) ).
fof(f57,plain,
( spl0_7
<=> c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f128,plain,
( spl0_13
<=> c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f136,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| spl0_1 ),
inference(resolution,[],[f19,f9]) ).
fof(f9,axiom,
! [X3,X6,X4,X5] :
( c_in(c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3),c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X5,X4,X3),X6,tc_set(tc_set(X3)))
| c_lessequals(X6,X4,tc_set(tc_set(X3)))
| ~ c_in(X6,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f134,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_6
| spl0_14
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f119,f57,f132,f53,f128,f90]) ).
fof(f90,plain,
( spl0_12
<=> c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f53,plain,
( spl0_6
<=> v_x = c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f119,plain,
! [X0] :
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| v_x = c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a)
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f12,f6]) ).
fof(f6,axiom,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = X0
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f12,axiom,
! [X3,X6,X4,X5] :
( ~ c_lessequals(c_Zorn_Osucc(X5,c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3),X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X5,X4,X3),X6,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| c_lessequals(X6,X4,tc_set(tc_set(X3)))
| ~ c_in(X6,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f111,plain,
spl0_4,
inference(avatar_split_clause,[],[f2,f34]) ).
fof(f2,axiom,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f110,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f4,f21]) ).
fof(f21,plain,
( spl0_2
<=> v_xa = c_Zorn_Osucc(v_S,v_x,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f4,axiom,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f109,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f108,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f98,f8]) ).
fof(f8,axiom,
! [X2,X3] : c_lessequals(X2,X2,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f98,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| ~ spl0_3 ),
inference(backward_demodulation,[],[f5,f32]) ).
fof(f32,plain,
( v_x = v_xa
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f30,plain,
( spl0_3
<=> v_x = v_xa ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f5,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f93,plain,
( spl0_12
| spl0_5
| ~ spl0_7
| ~ spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f77,f17,f34,f57,f38,f90]) ).
fof(f77,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(resolution,[],[f10,f19]) ).
fof(f10,axiom,
! [X3,X6,X4,X5] :
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3),X4,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X5,X4,X3),X6,tc_set(tc_set(X3)))
| c_lessequals(X6,X4,tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(X6,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f88,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f87,plain,
( $false
| spl0_7 ),
inference(resolution,[],[f59,f1]) ).
fof(f1,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f59,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| spl0_7 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_4
| ~ spl0_7
| spl0_1 ),
inference(avatar_split_clause,[],[f48,f17,f57,f34,f53,f38]) ).
fof(f48,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x != c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a)
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(resolution,[],[f11,f19]) ).
fof(f11,axiom,
! [X3,X6,X4,X5] :
( c_lessequals(c_Zorn_Osucc(X5,X4,X3),X6,tc_set(tc_set(X3)))
| ~ c_in(X6,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3) != X4
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| c_lessequals(X6,X4,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f41,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f27,f38,f34,f30]) ).
fof(f27,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_x = v_xa ),
inference(resolution,[],[f6,f25]) ).
fof(f25,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[],[f13,f5]) ).
fof(f13,axiom,
! [X3,X8,X7,X5] :
( c_lessequals(X7,c_Zorn_Osucc(X5,X8,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(X7,X8,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f24,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f15,f21,f17]) ).
fof(f15,plain,
( v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f7,f3]) ).
fof(f3,axiom,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,axiom,
! [X2,X3,X1] :
( ~ c_lessequals(X2,X1,tc_set(X3))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET853-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % 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 : n002.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 14:37:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.48 % (30278)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)
% 0.20/0.50 % (30275)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)
% 0.20/0.50 % (30283)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50 % (30297)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)
% 0.20/0.50 % (30286)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (30282)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)
% 0.20/0.51 % (30283)First to succeed.
% 0.20/0.51 % (30277)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (30281)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (30283)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (30283)------------------------------
% 0.20/0.51 % (30283)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (30283)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (30283)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (30283)Memory used [KB]: 5500
% 0.20/0.51 % (30283)Time elapsed: 0.101 s
% 0.20/0.51 % (30283)Instructions burned: 6 (million)
% 0.20/0.51 % (30283)------------------------------
% 0.20/0.51 % (30283)------------------------------
% 0.20/0.51 % (30272)Success in time 0.161 s
%------------------------------------------------------------------------------