%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL441-2 : 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 : n015.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 11:52:26 AM UTC 2026
% Result : Unsatisfiable 2.72s 1.35s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 7 unt; 2 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 10 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f2,axiom,
! [X2,X0,X1] :
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f3,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f5,definition,
( spl0_1
<=> c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f9,definition,
( spl0_2
<=> c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f11,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| spl0_2 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f12,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f1,f9,f5]) ).
fof(f13,plain,
( ~ c_in(c_PropLog_Opl_Ovar(v_a,t_a),c_insert(c_PropLog_Opl_Ovar(v_a,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| spl0_1 ),
inference(resolution,[],[f2,f7]) ).
fof(f14,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f13,f3]) ).
fof(f15,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f14]) ).
fof(f16,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_a,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_PropLog_Opl(t_a))
| spl0_2 ),
inference(resolution,[],[f11,f2]) ).
fof(f17,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f16,f3]) ).
fof(f18,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f17]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f12]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f15]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f18]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f19,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.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 : Sun Sep 27 15:46:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.72/1.35 % (1811197)Input is clausal, will run a generic CNF schedule.
% 2.72/1.35 % (1811205)lrs+10_1_sil=8000:sp=occurrence:random_seed=546492053:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.35 % (1811205)First to succeed.
% 2.72/1.35 % (1811205)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1811197"
% 2.72/1.35 % (1811204)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4177848649:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.35 % (1811206)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2815861289:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.35 % (1811208)dis-21_1_sil=8000:lcm=predicate:random_seed=588419526: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)
% 2.72/1.35 % (1811202)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=1800632439:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.35 % (1811203)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2622299368:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.35 % (1811207)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1041065808:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.35 % (1811208)Also succeeded, but the first one will report.
% 2.72/1.35 % (1811206)Also succeeded, but the first one will report.
% 2.72/1.35 % (1811207)Also succeeded, but the first one will report.
% 2.72/1.35 % (1811205)Refutation found. Thanks to Tanya!
% 2.72/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.35 % (1811205)------------------------------
% 2.72/1.35 % (1811205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (1811205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (1811205)CaDiCaL version: 2.1.3
% 2.72/1.35 % (1811205)Termination reason: Refutation
% 2.72/1.35 % (1811205)Time elapsed: 0.001 s
% 2.72/1.35 % (1811205)Peak memory usage: 89 MB
% 2.72/1.35 % (1811205)Instructions burned: 1 (million)
% 2.72/1.35 % (1811205)------------------------------
% 2.72/1.35 % (1811205)------------------------------
% 2.72/1.35 % (1811197)Success in time 0.3 s
% 2.72/1.35 % Vampire exiting
%------------------------------------------------------------------------------