%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET843-2 : 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 : n015.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 12:44:47 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 11 unt; 2 def)
% Number of atoms : 88 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 40 ~; 42 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,X1,tc_set(X2))
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f3,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f5,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(f6,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Osucc(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2))))
| c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_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)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
fof(f9,plain,
! [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_Osucc(X1,X0,X2) != X0
| c_lessequals(X3,X0,tc_set(tc_set(X2))) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f11,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f14,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(f15,plain,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f16,plain,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f18,definition,
( spl0_2
<=> v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f19,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f20,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f18,f14]) ).
fof(f22,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f11,f14,f18]) ).
fof(f24,plain,
c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolution,[],[f1,f10]) ).
fof(f27,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(resolution,[],[f3,f24]) ).
fof(f28,plain,
( ~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f27,f15]) ).
fof(f29,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolution,[],[f6,f10]) ).
fof(f31,plain,
! [X0,X1] : c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))),
inference(resolution,[],[f7,f4]) ).
fof(f34,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f9,f10]) ).
fof(f36,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_2 ),
inference(forward_subsumption_resolution,[],[f34,f20]) ).
fof(f38,plain,
( c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| ~ spl0_2 ),
inference(resolution,[],[f36,f31]) ).
fof(f39,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f38,f28]) ).
fof(f40,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f39]) ).
fof(f45,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolution,[],[f29,f1]) ).
fof(f46,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f45,f16]) ).
fof(f56,plain,
( ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_1 ),
inference(resolution,[],[f46,f3]) ).
fof(f57,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f56,f5]) ).
fof(f60,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f57,f19]) ).
fof(f61,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s1,s3]) ).
cnf(s8,plain,
spl0_2,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s8,s7]) ).
fof(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:02:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.44 % (2218495)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (2218505)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1925470219:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.44 % (2218500)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=18988975_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.44 % (2218503)dis+10_1_sil=32000:sp=arity:random_seed=1084825447:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.44 % (2218502)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1099409204:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (2218501)% WARNING: option uhcvi not known.
% 0.09/0.44 % (2218504)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2455956635:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.44 % (2218506)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=929545870:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % TRYING [1]
% 0.09/0.44 % (2218505) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2218495-2218505"...
% 0.09/0.44 % TRYING [2]
% 0.09/0.44 % (2218503) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2218495-2218503"...
% 0.09/0.44 % TRYING [3]
% 0.09/0.44 % (2218505)...printing done.
% 0.09/0.44 % (2218506) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2218495-2218506"...
% 0.09/0.44 % (2218503)...printing done.
% 0.09/0.44 % (2218505)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (2218505)------------------------------
% 0.09/0.44 % (2218505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (2218505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (2218505)CaDiCaL version: 2.1.3
% 0.09/0.44 % (2218505)Termination reason: Refutation
% 0.09/0.44 % (2218505)Time elapsed: 0.003 s
% 0.09/0.44 % (2218505)Peak memory usage: 12 MB
% 0.09/0.44 % (2218505)Instructions burned: 3 (million)
% 0.09/0.44 % (2218495)Success in time 0.041 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------