%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET853-2 : 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 : n005.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 12:44:50 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 15 unt; 2 def)
% Number of atoms : 99 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 109 ( 50 ~; 57 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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_0) ).
fof(f2,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,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_4) ).
fof(f6,negated_conjecture,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a)))
| X0 = v_x
| ~ c_lessequals(X0,v_x,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(f7,plain,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_x,tc_set(tc_set(t_a)))
| v_x = X0
| ~ c_lessequals(X0,v_x,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,[],[f6]) ).
fof(f8,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(f9,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f11,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(f12,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(f13,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(f14,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(f15,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(f16,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a) ),
inference(resolution,[],[f9,f3]) ).
fof(f19,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution,[],[f16,f4]) ).
fof(f20,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[],[f15,f5]) ).
fof(f22,plain,
( v_x = v_xa
| ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f20,f7]) ).
fof(f23,plain,
( v_x = v_xa
| ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f22,f2]) ).
fof(f25,definition,
( spl0_1
<=> c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,definition,
( spl0_2
<=> v_x = v_xa ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f31,plain,
( v_x = v_xa
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f29,f25]) ).
fof(f51,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| v_x = c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a)
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f14,f7]) ).
fof(f56,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f51,f13]) ).
fof(f57,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f56,f12]) ).
fof(f58,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f57,f11]) ).
fof(f59,plain,
! [X0] :
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f58,f1]) ).
fof(f60,plain,
( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f59,f19]) ).
fof(f65,plain,
c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution,[],[f60,f2]) ).
fof(f66,plain,
spl0_1,
inference(avatar_split_clause,[],[f65,f25]) ).
fof(f75,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_2 ),
inference(superposition,[],[f5,f31]) ).
fof(f78,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f75,f10]) ).
fof(f79,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f78]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f66]) ).
cnf(s5,plain,
~ spl0_2,
inference(sat_conversion,[],[f79]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
fof(f80,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET853-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:00:46 UTC 2026
% 0.05/0.38 % CPUTime :
% 0.05/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.05/0.41 Running first-order model finding
% 0.05/0.41 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
% 0.17/0.46 % (389062)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (389067)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=562500538_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % (389068)% WARNING: option uhcvi not known.
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % TRYING [4]
% 0.17/0.46 % (389068)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1876901134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (389072)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3189938254:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (389069)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1574435130:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (389070)dis+10_1_sil=32000:sp=arity:random_seed=3424816268:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (389071)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1463205518:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (389073)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=504184009:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (389070) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-389062-389070"...
% 0.17/0.46 % (389070)...printing done.
% 0.17/0.46 % (389072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-389062-389072"...
% 0.17/0.46 % (389070)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (389070)------------------------------
% 0.17/0.46 % (389070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (389070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (389070)CaDiCaL version: 2.1.3
% 0.17/0.46 % (389070)Termination reason: Refutation
% 0.17/0.46 % (389070)Time elapsed: 0.004 s
% 0.17/0.46 % (389070)Peak memory usage: 12 MB
% 0.17/0.46 % (389070)Instructions burned: 4 (million)
% 0.17/0.46 % (389062)Success in time 0.041 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------