%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 13 unt; 2 def)
% Number of atoms : 136 ( 8 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 151 ( 64 ~; 85 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f4,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,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_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( 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)))
| c_lessequals(X3,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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ 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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f8,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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f9,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f10,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f11,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f12,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f13,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f14,negated_conjecture,
! [X0,X1] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| X0 = X1
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f15,plain,
( v_n = v_x
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f14,f13]) ).
fof(f16,plain,
( v_n = v_x
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f15,f10]) ).
fof(f17,plain,
( v_n = v_x
| ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f16,f11]) ).
fof(f19,definition,
( spl0_1
<=> c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f21,plain,
( ~ c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl0_2
<=> v_n = v_x ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f25,plain,
( v_n = v_x
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f23,f19]) ).
fof(f27,plain,
! [X0,X1] :
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) ),
inference(resolution,[],[f3,f2]) ).
fof(f28,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(duplicate_literal_removal,[],[f27]) ).
fof(f29,plain,
! [X0] :
( c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1,f9]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( c_in(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(resolution,[],[f1,f4]) ).
fof(f44,plain,
! [X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X0,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f8,f14]) ).
fof(f48,plain,
! [X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f44,f7]) ).
fof(f49,plain,
! [X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f48,f5]) ).
fof(f50,plain,
! [X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f49,f6]) ).
fof(f51,plain,
! [X0,X1] :
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f50,f29]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ c_in(X2,c_Zorn_Osucc(v_S,X1,t_a),tc_set(t_a))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_in(X2,X0,tc_set(t_a)) ),
inference(resolution,[],[f51,f1]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| c_in(X2,X0,tc_set(t_a))
| ~ c_in(X2,X1,tc_set(t_a)) ),
inference(resolution,[],[f54,f31]) ).
fof(f73,plain,
! [X0,X1] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X0,tc_set(tc_set(t_a)))
| c_in(X1,v_n,tc_set(t_a))
| ~ c_in(X1,X0,tc_set(t_a)) ),
inference(resolution,[],[f69,f10]) ).
fof(f79,plain,
! [X0] :
( c_lessequals(v_n,v_x,tc_set(tc_set(t_a)))
| c_in(X0,v_n,tc_set(t_a))
| ~ c_in(X0,v_x,tc_set(t_a)) ),
inference(resolution,[],[f73,f11]) ).
fof(f81,plain,
( ! [X0] :
( ~ c_in(X0,v_x,tc_set(t_a))
| c_in(X0,v_n,tc_set(t_a)) )
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f79,f21]) ).
fof(f86,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x,X0,tc_set(t_a)),v_n,tc_set(t_a))
| c_lessequals(v_x,X0,tc_set(tc_set(t_a))) )
| spl0_1 ),
inference(resolution,[],[f81,f2]) ).
fof(f89,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(resolution,[],[f86,f3]) ).
fof(f90,plain,
( c_lessequals(v_x,v_n,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(duplicate_literal_removal,[],[f89]) ).
fof(f91,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f90,f12]) ).
fof(f92,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f98,plain,
( ~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(superposition,[],[f12,f25]) ).
fof(f102,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f98,f28]) ).
fof(f103,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f102]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f92]) ).
cnf(s6,plain,
~ spl0_2,
inference(sat_conversion,[],[f103]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s3]) ).
fof(f104,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:05:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.47 % (4114362)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (4114368)% WARNING: option uhcvi not known.
% 0.15/0.47 % (4114368)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2707854080:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (4114371)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2821265643:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (4114367)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1246224565_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (4114369)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=964521967:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (4114370)dis+10_1_sil=32000:sp=arity:random_seed=1127633821:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (4114372)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2936519245:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % (4114373)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3823195654:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (4114370) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4114362-4114370"...
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (4114370)...printing done.
% 0.15/0.47 % (4114370)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (4114370)------------------------------
% 0.15/0.47 % (4114370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (4114370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (4114370)CaDiCaL version: 2.1.3
% 0.15/0.47 % (4114370)Termination reason: Refutation
% 0.15/0.47 % (4114370)Time elapsed: 0.007 s
% 0.15/0.47 % (4114370)Peak memory usage: 12 MB
% 0.15/0.47 % (4114370)Instructions burned: 8 (million)
% 0.15/0.47 % (4114362)Success in time 0.057 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------