%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET853-1 : 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 : n009.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 2.65s 1.37s
% Output : Refutation 2.65s
% 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(f381,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f381]) ).
fof(f383,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f1435,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f1436,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f1437,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f1438,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(f1442,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f1443,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1444,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1445,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1446,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1447,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1448,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1449,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,[],[f1448]) ).
fof(f1454,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,[],[f382,f1445]) ).
fof(f1458,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))),
inference(forward_subsumption_resolution,[],[f1454,f1446]) ).
fof(f1459,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[],[f1442,f1447]) ).
fof(f1462,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,[],[f1459,f1449]) ).
fof(f1463,plain,
( v_x = v_xa
| ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[],[f1462,f1444]) ).
fof(f1465,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(f1467,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| spl0_1 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f1469,definition,
( spl0_2
<=> v_x = v_xa ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1471,plain,
( v_x = v_xa
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f1472,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1463,f1469,f1465]) ).
fof(f1493,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,[],[f1438,f1449]) ).
fof(f1498,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,[],[f1493,f1436]) ).
fof(f1500,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,[],[f1498,f1435]) ).
fof(f1501,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,[],[f1500,f1437]) ).
fof(f1502,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,[],[f1501,f1443]) ).
fof(f1503,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,[],[f1502,f1458]) ).
fof(f1506,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1503,f1467]) ).
fof(f1507,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1506,f1444]) ).
fof(f1508,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1507]) ).
fof(f1514,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,[],[f1447,f1471]) ).
fof(f1517,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1514,f383]) ).
fof(f1518,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f1517]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1472]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f1508]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f1518]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f1519,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET853-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.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 03:01:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.65/1.37 % (2623004)Input is clausal, will run a generic CNF schedule.
% 2.65/1.37 % (2623012)lrs+10_1_sil=8000:sp=occurrence:random_seed=4178592208:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.37 % (2623012)First to succeed.
% 2.65/1.37 % (2623012)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2623004"
% 2.65/1.37 % (2623009)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=3644137377:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.37 % (2623011)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=384400488:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.37 % (2623010)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4131527484:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.37 % (2623013)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2527517547:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.37 % (2623015)dis-21_1_sil=8000:lcm=predicate:random_seed=1845073906: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)
% 2.65/1.37 % (2623014)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3449666304:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.37 % (2623014)Also succeeded, but the first one will report.
% 2.65/1.37 % (2623013)Instruction limit reached!
% 2.65/1.37 % (2623013)------------------------------
% 2.65/1.37 % (2623013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (2623013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (2623013)CaDiCaL version: 2.1.3
% 2.65/1.37 % (2623013)Termination reason: Instruction limit
% 2.65/1.37 % (2623013)Termination phase: Saturation
% 2.65/1.37 % (2623013)Time elapsed: 0.068 s
% 2.65/1.37 % (2623013)Peak memory usage: 89 MB
% 2.65/1.37 % (2623013)Instructions burned: 117 (million)
% 2.65/1.37 % (2623015)Instruction limit reached!
% 2.65/1.37 % (2623015)------------------------------
% 2.65/1.37 % (2623015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (2623015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (2623015)CaDiCaL version: 2.1.3
% 2.65/1.37 % (2623015)Termination reason: Instruction limit
% 2.65/1.37 % (2623015)Termination phase: Saturation
% 2.65/1.37 % (2623015)Time elapsed: 0.069 s
% 2.65/1.37 % (2623015)Peak memory usage: 90 MB
% 2.65/1.37 % (2623015)Instructions burned: 118 (million)
% 2.65/1.37 % (2623012)Refutation found. Thanks to Tanya!
% 2.65/1.37 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.37 % (2623012)------------------------------
% 2.65/1.37 % (2623012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.37 % (2623012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.37 % (2623012)CaDiCaL version: 2.1.3
% 2.65/1.37 % (2623012)Termination reason: Refutation
% 2.65/1.37 % (2623012)Time elapsed: 0.004 s
% 2.65/1.37 % (2623012)Peak memory usage: 90 MB
% 2.65/1.37 % (2623012)Instructions burned: 8 (million)
% 2.65/1.37 % (2623012)------------------------------
% 2.65/1.37 % (2623012)------------------------------
% 2.65/1.37 % (2623004)Success in time 0.311 s
% 2.65/1.37 % Vampire exiting
%------------------------------------------------------------------------------