%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET858-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:10 PM UTC 2026
% Result : Unsatisfiable 2.81s 1.42s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 73 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 94 ( 43 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1434,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f1435,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f1436,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_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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f1437,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,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)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f1438,axiom,
! [X2,X3,X0,X1] :
( 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_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| 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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f1439,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f1440,axiom,
! [X2,X3,X0,X1] :
( 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(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| X0 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
fof(f1441,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1442,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1443,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1444,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1745,plain,
! [X0] :
( ~ c_lessequals(v_m,X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1434,f1444]) ).
fof(f1779,plain,
! [X0] : ~ c_lessequals(c_Zorn_Osucc(X0,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolution,[],[f1745,f1435]) ).
fof(f1825,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_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(resolution,[],[f1439,f1440]) ).
fof(f1828,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_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2) = X3 ),
inference(duplicate_literal_removal,[],[f1825]) ).
fof(f1830,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_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(forward_subsumption_resolution,[],[f1828,f1438]) ).
fof(f1832,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_lessequals(X0,X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X3,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(forward_subsumption_resolution,[],[f1830,f1437]) ).
fof(f1833,plain,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X3,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(forward_subsumption_resolution,[],[f1832,f1436]) ).
fof(f2070,plain,
! [X0] :
( ~ c_in(v_m,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1833,f1779]) ).
fof(f2097,plain,
! [X0] :
( ~ c_in(v_n,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f2070,f1443]) ).
fof(f2099,plain,
~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(resolution,[],[f2097,f1442]) ).
fof(f2100,plain,
$false,
inference(forward_subsumption_resolution,[],[f2099,f1441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n008.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 03:03:39 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.81/1.42 % (1825462)Input is clausal, will run a generic CNF schedule.
% 2.81/1.42 % (1825471)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1107432188:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.81/1.42 % (1825471)First to succeed.
% 2.81/1.42 % (1825471)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1825462"
% 2.81/1.42 % (1825467)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=221437922:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.81/1.42 % (1825469)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=777865034:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.81/1.42 % (1825468)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2233516283:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.81/1.42 % (1825470)lrs+10_1_sil=8000:sp=occurrence:random_seed=263300095:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.81/1.42 % (1825472)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1083153703:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.81/1.42 % (1825473)dis-21_1_sil=8000:lcm=predicate:random_seed=1811145823: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)
% 2.81/1.42 % (1825470)Also succeeded, but the first one will report.
% 2.81/1.42 % (1825473)Instruction limit reached!
% 2.81/1.42 % (1825473)------------------------------
% 2.81/1.42 % (1825473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.42 % (1825473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.42 % (1825473)CaDiCaL version: 2.1.3
% 2.81/1.42 % (1825473)Termination reason: Instruction limit
% 2.81/1.42 % (1825473)Termination phase: Saturation
% 2.81/1.42 % (1825473)Time elapsed: 0.068 s
% 2.81/1.42 % (1825473)Peak memory usage: 89 MB
% 2.81/1.42 % (1825473)Instructions burned: 117 (million)
% 2.81/1.42 % (1825471)Refutation found. Thanks to Tanya!
% 2.81/1.42 % SZS status Unsatisfiable for theBenchmark
% 2.81/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.42 % (1825471)------------------------------
% 2.81/1.42 % (1825471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.42 % (1825471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.42 % (1825471)CaDiCaL version: 2.1.3
% 2.81/1.42 % (1825471)Termination reason: Refutation
% 2.81/1.42 % (1825471)Time elapsed: 0.015 s
% 2.81/1.42 % (1825471)Peak memory usage: 89 MB
% 2.81/1.42 % (1825471)Instructions burned: 39 (million)
% 2.81/1.42 % (1825471)------------------------------
% 2.81/1.42 % (1825471)------------------------------
% 2.81/1.42 % (1825462)Success in time 0.327 s
% 2.81/1.42 % Vampire exiting
%------------------------------------------------------------------------------