%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET852-1 : 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 : 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 12:42:08 PM UTC 2026
% Result : Unsatisfiable 3.78s 1.46s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 10 unt; 2 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 30 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f378,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f383,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f1434,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
fof(f1435,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
fof(f1436,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
fof(f1440,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1441,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1442,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1464,plain,
! [X0,X1] :
( c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X1,X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_Y,tc_set(tc_set(tc_set(t_a))))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f378,f1442]) ).
fof(f1537,plain,
! [X0] :
( c_in(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1434,f1441]) ).
fof(f1539,plain,
! [X0] :
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1435,f1441]) ).
fof(f1541,plain,
! [X0] :
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1436,f1441]) ).
fof(f1544,plain,
~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolution,[],[f1539,f1440]) ).
fof(f1556,plain,
! [X0] :
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_Y,tc_set(tc_set(tc_set(t_a))))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[],[f1464,f1544]) ).
fof(f1559,definition,
( spl0_5
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f1561,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1563,definition,
( spl0_6
<=> ! [X0] :
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_Y,tc_set(tc_set(tc_set(t_a)))) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f1564,plain,
( ! [X0] :
( ~ c_lessequals(X0,v_Y,tc_set(tc_set(tc_set(t_a))))
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f1563]) ).
fof(f1565,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f1556,f1563,f1559]) ).
fof(f1597,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| ~ spl0_5 ),
inference(resolution,[],[f1561,f1541]) ).
fof(f1608,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1597,f1440]) ).
fof(f1609,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f1608]) ).
fof(f1682,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ spl0_6 ),
inference(resolution,[],[f1564,f383]) ).
fof(f1687,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| ~ spl0_6 ),
inference(resolution,[],[f1682,f1537]) ).
fof(f1689,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f1687,f1440]) ).
fof(f1690,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f1689]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f1565]) ).
cnf(s7,plain,
~ spl0_5,
inference(sat_conversion,[],[f1609]) ).
cnf(s10,plain,
~ spl0_6,
inference(sat_conversion,[],[f1690]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s10,s7]) ).
fof(f1691,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET852-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:02:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.78/1.46 % (1823809)Input is clausal, will run a generic CNF schedule.
% 3.78/1.46 % (1823820)dis-21_1_sil=8000:lcm=predicate:random_seed=2836153423: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)
% 3.78/1.46 % (1823815)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1799577051:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.78/1.46 % (1823814)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=2361141682:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.78/1.46 % (1823816)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2052044787:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.78/1.46 % (1823818)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3869530084:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.78/1.46 % (1823817)lrs+10_1_sil=8000:sp=occurrence:random_seed=1495952956:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.78/1.46 % (1823819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2753155700:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.78/1.46 % (1823820)Instruction limit reached!
% 3.78/1.46 % (1823820)------------------------------
% 3.78/1.46 % (1823820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.46 % (1823820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.46 % (1823820)CaDiCaL version: 2.1.3
% 3.78/1.46 % (1823820)Termination reason: Instruction limit
% 3.78/1.46 % (1823820)Termination phase: Saturation
% 3.78/1.46 % (1823820)Time elapsed: 0.038 s
% 3.78/1.46 % (1823820)Peak memory usage: 90 MB
% 3.78/1.46 % (1823820)Instructions burned: 119 (million)
% 3.78/1.46 % (1823819)First to succeed.
% 3.78/1.46 % (1823819)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1823809"
% 3.78/1.46 % (1823817)Instruction limit reached!
% 3.78/1.46 % (1823817)------------------------------
% 3.78/1.46 % (1823817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.46 % (1823817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.46 % (1823817)CaDiCaL version: 2.1.3
% 3.78/1.46 % (1823817)Termination reason: Instruction limit
% 3.78/1.46 % (1823817)Termination phase: Saturation
% 3.78/1.46 % (1823817)Time elapsed: 0.062 s
% 3.78/1.46 % (1823817)Peak memory usage: 89 MB
% 3.78/1.46 % (1823817)Instructions burned: 107 (million)
% 3.78/1.46 % (1823818)Instruction limit reached!
% 3.78/1.46 % (1823818)------------------------------
% 3.78/1.46 % (1823818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.46 % (1823818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.46 % (1823818)CaDiCaL version: 2.1.3
% 3.78/1.46 % (1823818)Termination reason: Instruction limit
% 3.78/1.46 % (1823818)Termination phase: Saturation
% 3.78/1.46 % (1823818)Time elapsed: 0.069 s
% 3.78/1.46 % (1823818)Peak memory usage: 89 MB
% 3.78/1.46 % (1823818)Instructions burned: 114 (million)
% 3.78/1.46 % (1823828)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2091745834:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.78/1.46 % (1823828)Also succeeded, but the first one will report.
% 3.78/1.46 % (1823829)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2350091188:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.78/1.46 % (1823830)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1036438245:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.78/1.46 % (1823829)Also succeeded, but the first one will report.
% 3.78/1.46 % (1823830)Also succeeded, but the first one will report.
% 3.78/1.46 % (1823819)Refutation found. Thanks to Tanya!
% 3.78/1.46 % SZS status Unsatisfiable for theBenchmark
% 3.78/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.46 % (1823819)------------------------------
% 3.78/1.46 % (1823819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.46 % (1823819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.46 % (1823819)CaDiCaL version: 2.1.3
% 3.78/1.46 % (1823819)Termination reason: Refutation
% 3.78/1.46 % (1823819)Time elapsed: 0.023 s
% 3.78/1.46 % (1823819)Peak memory usage: 90 MB
% 3.78/1.46 % (1823819)Instructions burned: 34 (million)
% 3.78/1.46 % (1823819)------------------------------
% 3.78/1.46 % (1823819)------------------------------
% 3.78/1.46 % (1823809)Success in time 0.478 s
% 3.78/1.46 % Vampire exiting
%------------------------------------------------------------------------------