%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL121-2 : 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 : n026.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 09:38:03 AM UTC 2026
% Result : Unsatisfiable 2.67s 1.18s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 8 unt; 1 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 92 ( 52 ~; 39 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X3,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X4,c_Comb_Odiamond__strip__lemmaE__1(X0,X4,X3,X1),X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X4,X1,X1),c_Transitive__Closure_Ortrancl(X0,X1),tc_prod(X1,X1))
| ~ c_Comb_Odiamond(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Transitive__Closure_Ortrancl(X1,X2),tc_prod(X2,X2))
| ~ c_in(X0,X1,tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( c_in(c_Pair(X4,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X4,X0,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Transitive__Closure_Ortrancl(X3,X2),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
fof(f5,negated_conjecture,
c_Comb_Odiamond(v_r,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f6,negated_conjecture,
c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,negated_conjecture,
c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,negated_conjecture,
! [X0] :
( c_in(c_Pair(v_ya,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f9,negated_conjecture,
! [X0] :
( c_in(c_Pair(X0,v_x(X0),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f10,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f15,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_xaa,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X1,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f4,f10]) ).
fof(f46,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(resolution,[],[f15,f9]) ).
fof(f53,plain,
! [X0] :
( ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[],[f46,f7]) ).
fof(f70,plain,
! [X0] :
( ~ c_in(c_Pair(v_z,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(v_xaa),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[],[f53,f3]) ).
fof(f148,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) ),
inference(resolution,[],[f70,f1]) ).
fof(f151,plain,
! [X0,X1] :
( ~ c_in(c_Pair(v_x(v_xaa),c_Comb_Odiamond__strip__lemmaE__1(v_r,X0,v_z,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,X0,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[],[f148,f5]) ).
fof(f478,plain,
! [X0,X1] :
( ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_Comb_Odiamond(v_r,t_a) ),
inference(resolution,[],[f151,f2]) ).
fof(f479,plain,
! [X0,X1] :
( ~ c_in(c_Pair(X0,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ),
inference(forward_subsumption_resolution,[],[f478,f5]) ).
fof(f481,definition,
( spl0_22
<=> ! [X1] :
( ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f482,plain,
( ! [X1] :
( ~ c_in(c_Pair(X1,v_x(v_xaa),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X1,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f483,plain,
( spl0_22
| spl0_22 ),
inference(avatar_split_clause,[],[f479,f481,f481]) ).
fof(f505,plain,
( ~ c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ spl0_22 ),
inference(resolution,[],[f482,f8]) ).
fof(f509,plain,
( ~ c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f505,f6]) ).
fof(f510,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f509,f7]) ).
fof(f511,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f510]) ).
cnf(s18,plain,
( spl0_22
| spl0_22 ),
inference(sat_conversion,[],[f483]) ).
cnf(s19,plain,
spl0_22,
inference(rat,[],[s18]) ).
cnf(s23,plain,
~ spl0_22,
inference(sat_conversion,[],[f511]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s19,s23]) ).
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:43:57 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.67/1.18 % (106414)Input is clausal, will run a generic CNF schedule.
% 2.67/1.18 % (106526)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3818825682:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.67/1.18 % (106526)First to succeed.
% 2.67/1.18 % (106526)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-106414"
% 2.67/1.18 % (106522)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=1903813789:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.67/1.18 % (106523)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3721213768:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.67/1.18 % (106528)dis-21_1_sil=8000:lcm=predicate:random_seed=3254091266: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)
% 2.67/1.18 % (106525)lrs+10_1_sil=8000:sp=occurrence:random_seed=1706708446:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.67/1.18 % (106524)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3658706290:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.67/1.18 % (106527)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1796619071:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.67/1.18 % (106527)Also succeeded, but the first one will report.
% 2.67/1.18 % (106528)Also succeeded, but the first one will report.
% 2.67/1.18 % (106525)Instruction limit reached!
% 2.67/1.18 % (106525)------------------------------
% 2.67/1.18 % (106525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.18 % (106525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.18 % (106525)CaDiCaL version: 2.1.3
% 2.67/1.18 % (106525)Termination reason: Instruction limit
% 2.67/1.18 % (106525)Termination phase: Saturation
% 2.67/1.18 % (106525)Time elapsed: 0.071 s
% 2.67/1.18 % (106525)Peak memory usage: 89 MB
% 2.67/1.18 % (106525)Instructions burned: 109 (million)
% 2.67/1.18 % (106526)Refutation found. Thanks to Tanya!
% 2.67/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.18 % (106526)------------------------------
% 2.67/1.18 % (106526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.18 % (106526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.18 % (106526)CaDiCaL version: 2.1.3
% 2.67/1.18 % (106526)Termination reason: Refutation
% 2.67/1.18 % (106526)Time elapsed: 0.009 s
% 2.67/1.18 % (106526)Peak memory usage: 89 MB
% 2.67/1.18 % (106526)Instructions burned: 24 (million)
% 2.67/1.18 % (106526)------------------------------
% 2.67/1.18 % (106526)------------------------------
% 2.67/1.18 % (106414)Success in time 0.296 s
% 2.67/1.18 % Vampire exiting
%------------------------------------------------------------------------------