%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG436-1 : TPTP v9.3.1. Released v4.1.0.
% 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 09:20:01 AM UTC 2026
% Result : Unsatisfiable 2.58s 1.14s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 4 unt; 2 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 12 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f543,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f544,axiom,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f545,negated_conjecture,
( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f546,negated_conjecture,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f652,definition,
( spl0_1
<=> c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f655,definition,
( spl0_2
<=> c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f657,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f543,f655,f652]) ).
fof(f660,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f544,f652,f655]) ).
fof(f661,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f546,f655,f652]) ).
fof(f662,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f545,f652,f655]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f657]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f660]) ).
cnf(s3,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f661]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f662]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
~ spl0_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG436-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:26:27 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.58/1.14 % (9214)Input is clausal, will run a generic CNF schedule.
% 2.58/1.14 % (9223)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3263451232:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.58/1.14 % (9223)First to succeed.
% 2.58/1.14 % (9223)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9214"
% 2.58/1.14 % (9224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2848217341:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.58/1.14 % (9219)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=1291646615:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.58/1.14 % (9222)lrs+10_1_sil=8000:sp=occurrence:random_seed=1417074415:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.58/1.14 % (9220)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=515592559:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.58/1.14 % (9225)dis-21_1_sil=8000:lcm=predicate:random_seed=3643928399: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)
% 2.58/1.14 % (9221)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=264935339:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.58/1.14 % (9222)Also succeeded, but the first one will report.
% 2.58/1.14 % (9225)Also succeeded, but the first one will report.
% 2.58/1.14 % (9224)Also succeeded, but the first one will report.
% 2.58/1.14 % (9223)Refutation found. Thanks to Tanya!
% 2.58/1.14 % SZS status Unsatisfiable for theBenchmark
% 2.58/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.14 % (9223)------------------------------
% 2.58/1.14 % (9223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.14 % (9223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.14 % (9223)CaDiCaL version: 2.1.3
% 2.58/1.14 % (9223)Termination reason: Refutation
% 2.58/1.14 % (9223)Time elapsed: 0.003 s
% 2.58/1.14 % (9223)Peak memory usage: 89 MB
% 2.58/1.14 % (9223)Instructions burned: 6 (million)
% 2.58/1.14 % (9223)------------------------------
% 2.58/1.14 % (9223)------------------------------
% 2.58/1.14 % (9214)Success in time 0.285 s
% 2.58/1.14 % Vampire exiting
%------------------------------------------------------------------------------