%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:44:51 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 13 unt; 5 def)
% Number of atoms : 141 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 149 ( 61 ~; 83 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| c_lessequals(X3,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f6,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(f7,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)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f8,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)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f9,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)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ 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_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ 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_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| X0 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
fof(f19,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n != c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f9,f2]) ).
fof(f21,definition,
( spl0_1
<=> v_n = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f23,plain,
( v_n != c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a)
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f25,definition,
( spl0_2
<=> ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a))) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f26,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a))) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f27,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f19,f25,f21]) ).
fof(f37,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f8,f2]) ).
fof(f39,definition,
( spl0_5
<=> c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f41,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f37,f25,f39]) ).
fof(f49,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f7,f2]) ).
fof(f51,definition,
( spl0_7
<=> c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f53,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( spl0_7
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f25,f51]) ).
fof(f55,plain,
( ! [X0] :
( ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
| v_n = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) )
| ~ spl0_5 ),
inference(resolution,[],[f41,f11]) ).
fof(f58,plain,
( ! [X0] :
( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) )
| spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f55,f23]) ).
fof(f62,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(resolution,[],[f26,f1]) ).
fof(f73,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f62,f4]) ).
fof(f104,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_Zorn_Osucc(v_S,v_n,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) )
| ~ spl0_2 ),
inference(resolution,[],[f73,f5]) ).
fof(f239,definition,
( spl0_30
<=> c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f241,plain,
( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f258,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(resolution,[],[f104,f6]) ).
fof(f263,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f258,f3]) ).
fof(f264,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f266,plain,
( ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
| spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f53,f58]) ).
fof(f271,plain,
( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),t_a),v_n,tc_set(tc_set(t_a)))
| spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f266,f2]) ).
fof(f272,plain,
( spl0_30
| spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f271,f51,f39,f21,f239]) ).
fof(f301,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) )
| ~ spl0_30 ),
inference(resolution,[],[f241,f10]) ).
fof(f313,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) )
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f301,f2]) ).
fof(f314,plain,
( spl0_2
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f313,f239,f25]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
( spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f54]) ).
cnf(s29,plain,
~ spl0_2,
inference(sat_conversion,[],[f264]) ).
cnf(s31,plain,
( spl0_1
| ~ spl0_5
| ~ spl0_7
| spl0_30 ),
inference(sat_conversion,[],[f272]) ).
cnf(s35,plain,
( spl0_2
| ~ spl0_30 ),
inference(sat_conversion,[],[f314]) ).
cnf(s36,plain,
~ spl0_30,
inference(rat,[],[s35,s29]) ).
cnf(s39,plain,
spl0_7,
inference(rat,[],[s5,s29]) ).
cnf(s40,plain,
spl0_5,
inference(rat,[],[s3,s29]) ).
cnf(s41,plain,
spl0_1,
inference(rat,[],[s31,s36,s39,s40]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s1,s29,s41]) ).
fof(f315,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 % Computer : n002.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Mon Sep 28 03:05:37 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.46 Running first-order model finding
% 0.16/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.50 % (4114530)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (4114541)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3606598836:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (4114536)% WARNING: option uhcvi not known.
% 0.16/0.50 % (4114537)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3901243995:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (4114535)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=550754224_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (4114536)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3426090388:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (4114538)dis+10_1_sil=32000:sp=arity:random_seed=4093473561:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (4114539)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=456360986:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (4114540)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=66364778:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % TRYING [1]
% 0.16/0.50 % TRYING [2]
% 0.16/0.50 % TRYING [3]
% 0.16/0.50 % (4114540) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4114530-4114540"...
% 0.16/0.50 % (4114538) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4114530-4114538"...
% 0.16/0.50 % (4114540)...printing done.
% 0.16/0.50 % (4114538)...printing done.
% 0.16/0.50 % (4114540)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (4114540)------------------------------
% 0.16/0.50 % (4114540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (4114540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (4114540)CaDiCaL version: 2.1.3
% 0.16/0.50 % (4114540)Termination reason: Refutation
% 0.16/0.50 % (4114540)Time elapsed: 0.009 s
% 0.16/0.50 % (4114540)Peak memory usage: 12 MB
% 0.16/0.50 % (4114540)Instructions burned: 11 (million)
% 0.16/0.50 % (4114530)Success in time 0.033 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------