%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET843-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:42:06 PM UTC 2026
% Result : Unsatisfiable 2.66s 1.38s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 7 unt; 2 def)
% Number of atoms : 95 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 51 ~; 52 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f378,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(X0,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f381,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f381]) ).
fof(f383,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f1436,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
fof(f1437,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f1438,axiom,
! [X2,X0,X1] :
( c_in(c_Zorn_Osucc(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
fof(f1439,axiom,
! [X2,X0,X1] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f1440,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
fof(f1441,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_Osucc(X1,X0,X2) != X0
| c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
inference(reorient_equations,[],[f1440]) ).
fof(f1442,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1443,negated_conjecture,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1444,negated_conjecture,
( 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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1446,definition,
( spl0_1
<=> v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1447,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f1449,definition,
( spl0_2
<=> v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1451,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1444,f1449,f1446]) ).
fof(f1452,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f1454,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f1443,f1446,f1449]) ).
fof(f1749,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
| c_Union(X0,X1) = X2
| ~ c_in(X2,X0,tc_set(X1)) ),
inference(resolution,[],[f382,f1436]) ).
fof(f1750,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X1,tc_set(tc_set(X2)))
| c_Zorn_Osucc(X0,X1,X2) = X1 ),
inference(resolution,[],[f382,f1437]) ).
fof(f1794,plain,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X3,tc_set(X2)),X0,tc_set(tc_set(X2)))
| c_Zorn_Osucc(X1,X0,X2) != X0
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(resolution,[],[f1441,f1439]) ).
fof(f1973,plain,
! [X2,X3,X0,X1] :
( c_Zorn_Osucc(X0,X1,X2) != X1
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(tc_set(X2))))
| c_Union(X3,tc_set(X2)) = X1
| ~ c_in(X1,X3,tc_set(tc_set(X2))) ),
inference(resolution,[],[f1794,f1749]) ).
fof(f1982,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(tc_set(X2))))
| c_Zorn_Osucc(X0,X1,X2) != X1
| c_Union(X3,tc_set(X2)) = X1
| ~ c_in(X1,X3,tc_set(tc_set(X2))) ),
inference(forward_subsumption_resolution,[],[f1973,f378]) ).
fof(f2244,plain,
! [X2,X0,X1] :
( ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| c_Union(c_Zorn_OTFin(X0,X2),tc_set(X2)) = X1
| c_Zorn_Osucc(X0,X1,X2) != X1 ),
inference(resolution,[],[f1982,f383]) ).
fof(f2280,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolution,[],[f2244,f1442]) ).
fof(f2284,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f2280,f1446,f1449]) ).
fof(f2294,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))) )
| ~ spl0_1 ),
inference(superposition,[],[f1436,f1447]) ).
fof(f2296,plain,
( ! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )
| ~ spl0_1 ),
inference(resolution,[],[f2294,f1438]) ).
fof(f2313,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_1 ),
inference(resolution,[],[f2296,f1750]) ).
fof(f2318,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f2313,f1442]) ).
fof(f2319,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2318,f1452]) ).
fof(f2320,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f2319]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1451]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1454]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f2284]) ).
cnf(s5,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f2320]) ).
cnf(s6,plain,
spl0_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
spl0_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f2321,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET843-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:58:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.66/1.37 % (2976075)Input is clausal, will run a generic CNF schedule.
% 2.66/1.37 % (2976084)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3012385588:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.66/1.37 % (2976084)First to succeed.
% 2.66/1.37 % (2976084)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2976075"
% 2.66/1.37 % (2976082)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3680248636:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.66/1.37 % (2976083)lrs+10_1_sil=8000:sp=occurrence:random_seed=1141073836:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.66/1.37 % (2976081)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=69434407:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.66/1.37 % (2976080)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2032929928:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.66/1.37 % (2976085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=523590534:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.66/1.37 % (2976086)dis-21_1_sil=8000:lcm=predicate:random_seed=516685963:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.66/1.37 % (2976083)Also succeeded, but the first one will report.
% 2.66/1.37 % (2976085)Also succeeded, but the first one will report.
% 2.66/1.37 % (2976086)Instruction limit reached!
% 2.66/1.37 % (2976086)------------------------------
% 2.66/1.37 % (2976086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.37 % (2976086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.37 % (2976086)CaDiCaL version: 2.1.3
% 2.66/1.37 % (2976086)Termination reason: Instruction limit
% 2.66/1.37 % (2976086)Termination phase: Saturation
% 2.66/1.37 % (2976086)Time elapsed: 0.069 s
% 2.66/1.37 % (2976086)Peak memory usage: 90 MB
% 2.66/1.37 % (2976086)Instructions burned: 118 (million)
% 2.66/1.37 % (2976084)Refutation found. Thanks to Tanya!
% 2.66/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.66/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.38 % (2976084)------------------------------
% 2.66/1.38 % (2976084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.38 % (2976084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.38 % (2976084)CaDiCaL version: 2.1.3
% 2.66/1.38 % (2976084)Termination reason: Refutation
% 2.66/1.38 % (2976084)Time elapsed: 0.020 s
% 2.66/1.38 % (2976084)Peak memory usage: 90 MB
% 2.66/1.38 % (2976084)Instructions burned: 54 (million)
% 2.66/1.38 % (2976084)------------------------------
% 2.66/1.38 % (2976084)------------------------------
% 2.66/1.38 % (2976075)Success in time 0.313 s
% 2.66/1.38 % Vampire exiting
%------------------------------------------------------------------------------