%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n017.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 12:42:09 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.34s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 42 ( 14 unt; 2 def)
% Number of atoms : 104 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 50 ~; 60 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 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(f27,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
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)))
| v_x = c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,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,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)))
| v_x = c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) ),
inference(forward_subsumption_resolution,[],[f56,f11]) ).
fof(f59,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,[],[f58,f13]) ).
fof(f60,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,[],[f59,f1]) ).
fof(f61,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,[],[f60,f19]) ).
fof(f63,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f61,f27]) ).
fof(f64,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f63,f2]) ).
fof(f65,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f74,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(f77,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f74,f10]) ).
fof(f78,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f77]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f78]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f79,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.12/0.37 % Computer : n017.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 02:56:21 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.68/1.34 % (3170246)Input is clausal, will run a generic CNF schedule.
% 2.68/1.34 % (3170254)lrs+10_1_sil=8000:sp=occurrence:random_seed=89621808:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.34 % (3170254)First to succeed.
% 2.68/1.34 % (3170254)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3170246"
% 2.68/1.34 % (3170256)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1336285942:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.34 % (3170252)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2697451932:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.34 % (3170253)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4033205399:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.34 % (3170251)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=3624962820:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.34 % (3170257)dis-21_1_sil=8000:lcm=predicate:random_seed=1657310458: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)
% 2.68/1.34 % (3170255)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3551456245:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.34 % (3170257)Refutation not found, incomplete strategy
% 2.68/1.34 % (3170257)------------------------------
% 2.68/1.34 % (3170257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3170257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3170257)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3170257)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.34 % (3170257)Time elapsed: 0.003 s
% 2.68/1.34 % (3170257)Peak memory usage: 88 MB
% 2.68/1.34 % (3170257)Instructions burned: 3 (million)
% 2.68/1.34 % (3170256)Also succeeded, but the first one will report.
% 2.68/1.34 % (3170255)Also succeeded, but the first one will report.
% 2.68/1.34 % (3170254)Refutation found. Thanks to Tanya!
% 2.68/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (3170254)------------------------------
% 2.68/1.34 % (3170254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3170254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3170254)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3170254)Termination reason: Refutation
% 2.68/1.34 % (3170254)Time elapsed: 0.003 s
% 2.68/1.34 % (3170254)Peak memory usage: 89 MB
% 2.68/1.34 % (3170254)Instructions burned: 5 (million)
% 2.68/1.34 % (3170254)------------------------------
% 2.68/1.34 % (3170254)------------------------------
% 2.68/1.34 % (3170246)Success in time 0.291 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------