%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET848-2 : 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 : 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 12:42:07 PM UTC 2026
% Result : Unsatisfiable 3.55s 1.37s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 22 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)
| c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
fof(f2,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Zorn_Ochain(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__chain__lemma4_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_minus(c_Zorn_Ochain(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2)))
| c_Zorn_Osucc(X1,X0,X2) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
fof(f6,negated_conjecture,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f7,negated_conjecture,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f8,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
! [X2,X0,X1] :
( c_in(X1,c_Zorn_Omaxchain(X0,X2),tc_set(tc_set(X2)))
| c_Zorn_Osucc(X0,X1,X2) != X1
| ~ c_in(X1,c_Zorn_Ochain(X0,X2),tc_set(tc_set(X2))) ),
inference(resolution,[],[f5,f1]) ).
fof(f10,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)
| ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f9,f6]) ).
fof(f11,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution,[],[f10,f8]) ).
fof(f12,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolution,[],[f11,f4]) ).
fof(f13,plain,
~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(resolution,[],[f12,f3]) ).
fof(f14,plain,
$false,
inference(forward_subsumption_resolution,[],[f13,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET848-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:00:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 3.55/1.37 % (388265)Input is clausal, will run a generic CNF schedule.
% 3.55/1.37 % (388272)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2038724329:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/1.37 % (388270)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=502516605:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/1.37 % (388276)dis-21_1_sil=8000:lcm=predicate:random_seed=3915489397: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)
% 3.55/1.37 % (388271)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=873031285:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/1.37 % (388274)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=351874241:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/1.37 % (388273)lrs+10_1_sil=8000:sp=occurrence:random_seed=696251:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/1.37 % (388275)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3657736965:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/1.37 % (388273)Also succeeded, but the first one will report.
% 3.55/1.37 % (388274)First to succeed.
% 3.55/1.37 % (388276)Also succeeded, but the first one will report.
% 3.55/1.37 % (388274)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-388265"
% 3.55/1.37 % (388275)Also succeeded, but the first one will report.
% 3.55/1.37 % (388274)Refutation found. Thanks to Tanya!
% 3.55/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.37 % (388274)------------------------------
% 3.55/1.37 % (388274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.37 % (388274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.37 % (388274)CaDiCaL version: 2.1.3
% 3.55/1.37 % (388274)Termination reason: Refutation
% 3.55/1.37 % (388274)Time elapsed: 0.002 s
% 3.55/1.37 % (388274)Peak memory usage: 88 MB
% 3.55/1.37 % (388274)Instructions burned: 1 (million)
% 3.55/1.37 % (388274)------------------------------
% 3.55/1.37 % (388274)------------------------------
% 3.55/1.37 % (388265)Success in time 0.435 s
% 3.55/1.37 % Vampire exiting
%------------------------------------------------------------------------------