%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 3.64s 1.47s
% Output : Refutation 3.64s
% 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(f1,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f2,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f3,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f8,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,[],[f7]) ).
fof(f10,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(f14,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(f16,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,[],[f14]) ).
fof(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f6,f14,f10]) ).
fof(f18,plain,
( v_x = v_m
| ~ 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,[],[f8,f4]) ).
fof(f19,plain,
( v_x = v_m
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f18,f3]) ).
fof(f21,definition,
( spl0_3
<=> v_x = v_m ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f23,plain,
( v_x = v_m
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f24,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f19,f21,f10]) ).
fof(f25,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[],[f2,f5]) ).
fof(f26,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f25,f16]) ).
fof(f27,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f26]) ).
fof(f29,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(superposition,[],[f5,f23]) ).
fof(f31,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f29,f1]) ).
fof(f32,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
~ spl0_1,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:01:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.47 % (3621779)Input is clausal, will run a generic CNF schedule.
% 3.64/1.47 % (3621790)dis-21_1_sil=8000:lcm=predicate:random_seed=1660058116: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)
% 3.64/1.47 % (3621790)Refutation not found, incomplete strategy
% 3.64/1.47 % (3621790)------------------------------
% 3.64/1.47 % (3621790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.47 % (3621790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.47 % (3621790)CaDiCaL version: 2.1.3
% 3.64/1.47 % (3621790)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.47 % (3621790)Time elapsed: 0.001 s
% 3.64/1.47 % (3621790)Peak memory usage: 88 MB
% 3.64/1.47 % (3621787)lrs+10_1_sil=8000:sp=occurrence:random_seed=2477574076:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.64/1.47 % (3621786)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2553285514:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.64/1.47 % (3621785)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=291885468:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.64/1.47 % (3621788)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3870390329:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.64/1.47 % (3621784)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=4258432334:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.64/1.47 % (3621789)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4063252229:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.64/1.47 % (3621788)Also succeeded, but the first one will report.
% 3.64/1.47 % (3621787)First to succeed.
% 3.64/1.47 % (3621789)Also succeeded, but the first one will report.
% 3.64/1.47 % (3621787)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3621779"
% 3.64/1.47 % (3621790)------------------------------
% 3.64/1.47 % (3621790)------------------------------
% 3.64/1.47 % (3621787)Refutation found. Thanks to Tanya!
% 3.64/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.64/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.47 % (3621787)------------------------------
% 3.64/1.47 % (3621787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.47 % (3621787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.47 % (3621787)CaDiCaL version: 2.1.3
% 3.64/1.47 % (3621787)Termination reason: Refutation
% 3.64/1.47 % (3621787)Time elapsed: 0.002 s
% 3.64/1.47 % (3621787)Peak memory usage: 89 MB
% 3.64/1.47 % (3621787)Instructions burned: 1 (million)
% 3.64/1.47 % (3621787)------------------------------
% 3.64/1.47 % (3621787)------------------------------
% 3.64/1.47 % (3621779)Success in time 0.432 s
% 3.64/1.47 % Vampire exiting
%------------------------------------------------------------------------------