%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL445-2 : 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 : n018.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 11:52:27 AM UTC 2026
% Result : Unsatisfiable 2.22s 1.07s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 12 unt; 2 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 13 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(v_q,c_PropLog_Othms(c_insert(v_p,v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
c_in(v_q,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_H,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
~ c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),X1,X2),X1,X2),X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle_0) ).
fof(f7,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[],[f4,f1]) ).
fof(f8,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
inference(resolution,[],[f4,f2]) ).
fof(f12,plain,
! [X2,X3,X0,X1] :
( c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),X1,X2),X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
inference(resolution,[],[f5,f6]) ).
fof(f14,definition,
( spl0_1
<=> c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f15,plain,
( c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2))
| c_in(X1,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
inference(resolution,[],[f12,f5]) ).
fof(f34,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| c_in(v_q,c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[],[f26,f8]) ).
fof(f36,definition,
( spl0_4
<=> c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f37,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
| spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f38,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f34,f36,f14]) ).
fof(f39,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f37,f7]) ).
fof(f40,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f39]) ).
fof(f41,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f15,f3]) ).
fof(f42,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f41]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f42]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s4,s5]) ).
fof(f43,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n018.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 15:45:55 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 2.22/1.07 % (2536265)Input is clausal, will run a generic CNF schedule.
% 2.22/1.07 % (2536277)dis-21_1_sil=8000:lcm=predicate:random_seed=2352663414:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 2.22/1.07 % (2536277)First to succeed.
% 2.22/1.07 % (2536277)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2536265"
% 2.22/1.07 % (2536274)lrs+10_1_sil=8000:sp=occurrence:random_seed=3790919437:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 2.22/1.07 % (2536276)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=640329779:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 2.22/1.07 % (2536272)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3473890467:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 2.22/1.07 % (2536273)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1270970993:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 2.22/1.07 % (2536271)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=768867190:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 2.22/1.07 % (2536274)Also succeeded, but the first one will report.
% 2.22/1.07 % (2536276)Also succeeded, but the first one will report.
% 2.22/1.07 % (2536275)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3945035303:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 2.22/1.07 % (2536275)Also succeeded, but the first one will report.
% 2.22/1.07 % (2536277)Refutation found. Thanks to Tanya!
% 2.22/1.07 % SZS status Unsatisfiable for theBenchmark
% 2.22/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.22/1.07 % (2536277)------------------------------
% 2.22/1.07 % (2536277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/1.07 % (2536277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/1.07 % (2536277)CaDiCaL version: 2.1.3
% 2.22/1.07 % (2536277)Termination reason: Refutation
% 2.22/1.07 % (2536277)Time elapsed: 0.002 s
% 2.22/1.07 % (2536277)Peak memory usage: 89 MB
% 2.22/1.07 % (2536277)Instructions burned: 2 (million)
% 2.22/1.07 % (2536277)------------------------------
% 2.22/1.07 % (2536277)------------------------------
% 2.22/1.07 % (2536265)Success in time 0.253 s
% 2.22/1.07 % Vampire exiting
%------------------------------------------------------------------------------