%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET841-1 : 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 : n010.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 12:42:05 PM UTC 2026
% Result : Unsatisfiable 0.15s 1.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 13 unt; 1 def)
% Number of atoms : 37 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 14 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__subsetD_0) ).
fof(f1435,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1436,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1437,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_2) ).
fof(f1438,negated_conjecture,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1439,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1445,definition,
( spl0_1
<=> v_m = v_x ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1447,plain,
( v_m = v_x
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f1453,plain,
( ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = v_x ),
inference(resolution,[],[f1434,f1439]) ).
fof(f1457,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = v_x ),
inference(forward_subsumption_resolution,[],[f1453,f1435]) ).
fof(f1458,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_m = v_x ),
inference(forward_subsumption_resolution,[],[f1457,f1438]) ).
fof(f1459,plain,
v_m = v_x,
inference(forward_subsumption_resolution,[],[f1458,f1437]) ).
fof(f1460,plain,
spl0_1,
inference(avatar_split_clause,[],[f1459,f1445]) ).
fof(f1462,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| ~ spl0_1 ),
inference(superposition,[],[f1439,f1447]) ).
fof(f1465,plain,
( ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a)))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1462,f1436]) ).
fof(f1468,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1465,f383]) ).
fof(f1469,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1468]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1460]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f1469]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
fof(f1470,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET841-1 : 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 : n010.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 02:58:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.15/1.40 % (1518832)Input is clausal, will run a generic CNF schedule.
% 0.15/1.40 % (1518839)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2324495361:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.15/1.40 % (1518837)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=1965934636:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.15/1.40 % (1518841)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1293623914:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.15/1.40 % (1518838)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4134531966:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.15/1.40 % (1518843)dis-21_1_sil=8000:lcm=predicate:random_seed=1934318416: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)
% 0.15/1.40 % (1518842)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3286063261:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.15/1.40 % (1518840)lrs+10_1_sil=8000:sp=occurrence:random_seed=2311111901:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.15/1.40 % (1518840)First to succeed.
% 0.15/1.40 % (1518840)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1518832"
% 0.15/1.40 % (1518841)Also succeeded, but the first one will report.
% 0.15/1.40 % (1518842)Also succeeded, but the first one will report.
% 0.15/1.40 % (1518843)Instruction limit reached!
% 0.15/1.40 % (1518843)------------------------------
% 0.15/1.40 % (1518843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.40 % (1518843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.40 % (1518843)CaDiCaL version: 2.1.3
% 0.15/1.40 % (1518843)Termination reason: Instruction limit
% 0.15/1.40 % (1518843)Termination phase: Saturation
% 0.15/1.40 % (1518843)Time elapsed: 0.070 s
% 0.15/1.40 % (1518843)Peak memory usage: 89 MB
% 0.15/1.40 % (1518843)Instructions burned: 117 (million)
% 0.15/1.40 % (1518851)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=3229427263:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.15/1.40 % (1518851)Also succeeded, but the first one will report.
% 0.15/1.40 % (1518840)Refutation found. Thanks to Tanya!
% 0.15/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.40 % (1518840)------------------------------
% 0.15/1.40 % (1518840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.40 % (1518840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.40 % (1518840)CaDiCaL version: 2.1.3
% 0.15/1.40 % (1518840)Termination reason: Refutation
% 0.15/1.40 % (1518840)Time elapsed: 0.005 s
% 0.15/1.40 % (1518840)Peak memory usage: 90 MB
% 0.15/1.40 % (1518840)Instructions burned: 4 (million)
% 0.15/1.40 % (1518840)------------------------------
% 0.15/1.40 % (1518840)------------------------------
% 0.15/1.40 % (1518832)Success in time 0.465 s
% 0.15/1.40 % Vampire exiting
%------------------------------------------------------------------------------