%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET851-1 : 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 : n020.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 12:42:08 PM UTC 2026
% Result : Unsatisfiable 2.55s 1.34s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 12 unt; 3 def)
% Number of atoms : 53 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 24 ~; 20 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f1437,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f1439,negated_conjecture,
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_1) ).
fof(f1440,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1441,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,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_3) ).
fof(f1442,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1443,negated_conjecture,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
| X0 = v_m
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1444,plain,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
| v_m = X0
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(reorient_equations,[],[f1443]) ).
fof(f1446,definition,
( spl0_1
<=> c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1450,definition,
( spl0_2
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1452,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f1453,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1442,f1450,f1446]) ).
fof(f1454,plain,
( v_m = v_x
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1444,f1440]) ).
fof(f1455,plain,
( v_m = v_x
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f1454,f1439]) ).
fof(f1457,definition,
( spl0_3
<=> v_m = v_x ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1459,plain,
( v_m = v_x
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f1460,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f1455,f1457,f1446]) ).
fof(f1476,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[],[f1437,f1441]) ).
fof(f1480,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1476,f1452]) ).
fof(f1481,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1480]) ).
fof(f1485,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| ~ spl0_3 ),
inference(superposition,[],[f1441,f1459]) ).
fof(f1488,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1485,f383]) ).
fof(f1489,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1488]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1453]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f1460]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f1481]) ).
cnf(s6,plain,
~ spl0_3,
inference(sat_conversion,[],[f1489]) ).
cnf(s7,plain,
~ spl0_1,
inference(rat,[],[s2,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s7]) ).
fof(f1490,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET851-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:01:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.55/1.34 % (3987753)Input is clausal, will run a generic CNF schedule.
% 2.55/1.34 % (3987761)lrs+10_1_sil=8000:sp=occurrence:random_seed=1886606615:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.55/1.34 % (3987761)First to succeed.
% 2.55/1.34 % (3987761)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3987753"
% 2.55/1.34 % (3987763)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3500433087:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/1.34 % (3987764)dis-21_1_sil=8000:lcm=predicate:random_seed=294877502: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)
% 2.55/1.34 % (3987759)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3038824010:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.55/1.34 % (3987760)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1763805780:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.55/1.34 % (3987758)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=2071936463:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.55/1.34 % (3987762)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1869827967:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.55/1.34 % (3987762)Also succeeded, but the first one will report.
% 2.55/1.34 % (3987763)Also succeeded, but the first one will report.
% 2.55/1.34 % (3987764)Instruction limit reached!
% 2.55/1.34 % (3987764)------------------------------
% 2.55/1.34 % (3987764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.34 % (3987764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.34 % (3987764)CaDiCaL version: 2.1.3
% 2.55/1.34 % (3987764)Termination reason: Instruction limit
% 2.55/1.34 % (3987764)Termination phase: Saturation
% 2.55/1.34 % (3987764)Time elapsed: 0.069 s
% 2.55/1.34 % (3987764)Peak memory usage: 90 MB
% 2.55/1.34 % (3987764)Instructions burned: 118 (million)
% 2.55/1.34 % (3987761)Refutation found. Thanks to Tanya!
% 2.55/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.55/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.34 % (3987761)------------------------------
% 2.55/1.34 % (3987761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.34 % (3987761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.34 % (3987761)CaDiCaL version: 2.1.3
% 2.55/1.34 % (3987761)Termination reason: Refutation
% 2.55/1.34 % (3987761)Time elapsed: 0.003 s
% 2.55/1.34 % (3987761)Peak memory usage: 90 MB
% 2.55/1.34 % (3987761)Instructions burned: 5 (million)
% 2.55/1.34 % (3987761)------------------------------
% 2.55/1.34 % (3987761)------------------------------
% 2.55/1.34 % (3987753)Success in time 0.297 s
% 2.55/1.34 % Vampire exiting
%------------------------------------------------------------------------------