%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR044+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:42:14 AM UTC 2026
% Result : Theorem 3.11s 1.11s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 17 unt; 5 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 152 ( 70 ~; 63 |; 6 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( isa(X0,X1)
& relationallexists(X2,X1,X3) )
=> isa(f_relationallexistsfn(X0,X2,X1,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just1) ).
fof(f8,axiom,
genlmt(c_tptp_spindleheadmt,c_cyclistsmt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just8) ).
fof(f9,axiom,
genlmt(c_tptp_member3633_mt,c_tptp_spindleheadmt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just9) ).
fof(f10,axiom,
! [X0] :
( ( mtvisible(c_cyclistsmt)
& executionbyfiringsquad(X0) )
=> tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just10) ).
fof(f11,axiom,
( mtvisible(c_cyclistsmt)
=> relationallexists(c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just11) ).
fof(f12,axiom,
executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just12) ).
fof(f31,axiom,
! [X0] :
( isa(X0,c_tptpcol_16_29490)
=> tptpcol_16_29490(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just31) ).
fof(f34,axiom,
! [X0] :
( executionbyfiringsquad(X0)
=> isa(X0,c_executionbyfiringsquad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just34) ).
fof(f48,axiom,
! [X0,X1] :
( ( mtvisible(X0)
& genlmt(X0,X1) )
=> mtvisible(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just48) ).
fof(f65,conjecture,
? [X0] :
( mtvisible(c_tptp_member3633_mt)
=> ( tptp_9_720(c_tptpexecutionbyfiringsquad_90,X0)
& tptpcol_16_29490(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query44) ).
fof(f66,negated_conjecture,
~ ? [X0] :
( mtvisible(c_tptp_member3633_mt)
=> ( tptp_9_720(c_tptpexecutionbyfiringsquad_90,X0)
& tptpcol_16_29490(X0) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( isa(f_relationallexistsfn(X0,X2,X1,X3),X3)
| ~ isa(X0,X1)
| ~ relationallexists(X2,X1,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( isa(f_relationallexistsfn(X0,X2,X1,X3),X3)
| ~ isa(X0,X1)
| ~ relationallexists(X2,X1,X3) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0] :
( tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490))
| ~ mtvisible(c_cyclistsmt)
| ~ executionbyfiringsquad(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f94,plain,
! [X0] :
( tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490))
| ~ mtvisible(c_cyclistsmt)
| ~ executionbyfiringsquad(X0) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
( relationallexists(c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490)
| ~ mtvisible(c_cyclistsmt) ),
inference(ennf_transformation,[],[f11]) ).
fof(f112,plain,
! [X0] :
( tptpcol_16_29490(X0)
| ~ isa(X0,c_tptpcol_16_29490) ),
inference(ennf_transformation,[],[f31]) ).
fof(f115,plain,
! [X0] :
( isa(X0,c_executionbyfiringsquad)
| ~ executionbyfiringsquad(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f119,plain,
! [X0,X1] :
( mtvisible(X1)
| ~ mtvisible(X0)
| ~ genlmt(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f120,plain,
! [X0,X1] :
( mtvisible(X1)
| ~ mtvisible(X0)
| ~ genlmt(X0,X1) ),
inference(flattening,[],[f119]) ).
fof(f129,plain,
! [X0] :
( ( ~ tptp_9_720(c_tptpexecutionbyfiringsquad_90,X0)
| ~ tptpcol_16_29490(X0) )
& mtvisible(c_tptp_member3633_mt) ),
inference(ennf_transformation,[],[f66]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( ~ relationallexists(X2,X1,X3)
| ~ isa(X0,X1)
| isa(f_relationallexistsfn(X0,X2,X1,X3),X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
genlmt(c_tptp_spindleheadmt,c_cyclistsmt),
inference(cnf_transformation,[],[f8]) ).
fof(f137,plain,
genlmt(c_tptp_member3633_mt,c_tptp_spindleheadmt),
inference(cnf_transformation,[],[f9]) ).
fof(f138,plain,
! [X0] :
( tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490))
| ~ mtvisible(c_cyclistsmt)
| ~ executionbyfiringsquad(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
( relationallexists(c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490)
| ~ mtvisible(c_cyclistsmt) ),
inference(cnf_transformation,[],[f95]) ).
fof(f140,plain,
executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90),
inference(cnf_transformation,[],[f12]) ).
fof(f153,plain,
! [X0] :
( tptpcol_16_29490(X0)
| ~ isa(X0,c_tptpcol_16_29490) ),
inference(cnf_transformation,[],[f112]) ).
fof(f156,plain,
! [X0] :
( ~ executionbyfiringsquad(X0)
| isa(X0,c_executionbyfiringsquad) ),
inference(cnf_transformation,[],[f115]) ).
fof(f161,plain,
! [X0,X1] :
( mtvisible(X1)
| ~ mtvisible(X0)
| ~ genlmt(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f170,plain,
mtvisible(c_tptp_member3633_mt),
inference(cnf_transformation,[],[f129]) ).
fof(f171,plain,
! [X0] :
( ~ tptpcol_16_29490(X0)
| ~ tptp_9_720(c_tptpexecutionbyfiringsquad_90,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f173,definition,
( spl0_1
<=> mtvisible(c_cyclistsmt) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f174,plain,
( ~ mtvisible(c_cyclistsmt)
| spl0_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,definition,
( spl0_2
<=> relationallexists(c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f177,plain,
( relationallexists(c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f178,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f139,f176,f173]) ).
fof(f180,definition,
( spl0_3
<=> ! [X0] :
( tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490))
| ~ executionbyfiringsquad(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f181,plain,
( ! [X0] :
( tptp_9_720(X0,f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490))
| ~ executionbyfiringsquad(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f182,plain,
( ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f138,f180,f173]) ).
fof(f185,plain,
! [X0] :
( ~ tptp_9_720(c_tptpexecutionbyfiringsquad_90,X0)
| ~ isa(X0,c_tptpcol_16_29490) ),
inference(resolution,[],[f153,f171]) ).
fof(f187,plain,
isa(c_tptpexecutionbyfiringsquad_90,c_executionbyfiringsquad),
inference(resolution,[],[f156,f140]) ).
fof(f193,plain,
( ! [X0] :
( ~ mtvisible(X0)
| ~ genlmt(X0,c_cyclistsmt) )
| spl0_1 ),
inference(resolution,[],[f161,f174]) ).
fof(f194,plain,
( ! [X0,X1] :
( ~ mtvisible(X1)
| ~ genlmt(X0,c_cyclistsmt)
| ~ genlmt(X1,X0) )
| spl0_1 ),
inference(resolution,[],[f193,f161]) ).
fof(f201,plain,
( ! [X0] :
( ~ genlmt(X0,c_cyclistsmt)
| ~ genlmt(c_tptp_member3633_mt,X0) )
| spl0_1 ),
inference(resolution,[],[f194,f170]) ).
fof(f202,plain,
( ~ genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
| spl0_1 ),
inference(resolution,[],[f201,f137]) ).
fof(f204,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f202,f136]) ).
fof(f205,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f206,plain,
( ~ executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90)
| ~ isa(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490),c_tptpcol_16_29490)
| ~ spl0_3 ),
inference(resolution,[],[f181,f185]) ).
fof(f209,definition,
( spl0_4
<=> isa(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490),c_tptpcol_16_29490) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f210,plain,
( ~ isa(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490),c_tptpcol_16_29490)
| spl0_4 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,definition,
( spl0_5
<=> executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f213,plain,
( ~ executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90)
| spl0_5 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f214,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f206,f180,f212,f209]) ).
fof(f216,plain,
( ! [X0] :
( isa(f_relationallexistsfn(X0,c_tptp_9_720,c_executionbyfiringsquad,c_tptpcol_16_29490),c_tptpcol_16_29490)
| ~ isa(X0,c_executionbyfiringsquad) )
| ~ spl0_2 ),
inference(resolution,[],[f130,f177]) ).
fof(f217,plain,
( ~ isa(c_tptpexecutionbyfiringsquad_90,c_executionbyfiringsquad)
| ~ spl0_2
| spl0_4 ),
inference(resolution,[],[f216,f210]) ).
fof(f218,plain,
( $false
| ~ spl0_2
| spl0_4 ),
inference(resolution,[],[f217,f187]) ).
fof(f219,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f220,plain,
( $false
| spl0_5 ),
inference(resolution,[],[f213,f140]) ).
fof(f222,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f220]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f182]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f205]) ).
cnf(s4,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f214]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f219]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f222]) ).
cnf(s7,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
spl0_3,
inference(rat,[],[s2,s3]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
~ spl0_2,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s3]) ).
fof(f223,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR044+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 22:18:10 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.11/1.11 % (3856818)Detected formulas, will run a generic FOF schedule.
% 3.11/1.11 % (3856882)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=622616394:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.11/1.11 % (3856882)Instruction limit reached!
% 3.11/1.11 % (3856882)------------------------------
% 3.11/1.11 % (3856882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.11 % (3856882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.11 % (3856882)CaDiCaL version: 2.1.3
% 3.11/1.11 % (3856882)Termination reason: Instruction limit
% 3.11/1.11 % (3856882)Termination phase: Saturation
% 3.11/1.11 % (3856882)Time elapsed: 0.025 s
% 3.11/1.11 % (3856882)Peak memory usage: 87 MB
% 3.11/1.11 % (3856882)Instructions burned: 121 (million)
% 3.11/1.11 % (3856874)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2316149344:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.11/1.11 % (3856886)dis-21_1_sil=8000:lcm=predicate:random_seed=1435070903:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.11/1.11 % (3856879)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1942163226:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.11/1.11 % (3856872)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=2586537999:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.11/1.11 % (3856879)Refutation not found, incomplete strategy
% 3.11/1.11 % (3856879)------------------------------
% 3.11/1.11 % (3856879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.11 % (3856879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.11 % (3856879)CaDiCaL version: 2.1.3
% 3.11/1.11 % (3856879)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.11 % (3856879)Time elapsed: 0.001 s
% 3.11/1.11 % (3856879)Peak memory usage: 87 MB
% 3.11/1.11 % (3856886)First to succeed.
% 3.11/1.11 % (3856886)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3856818"
% 3.11/1.11 % (3856883)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4075000751:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.11/1.11 % (3856878)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3749060250:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.11/1.11 % (3856883)Also succeeded, but the first one will report.
% 3.11/1.11 % (3856914)lrs+10_1_sil=8000:sp=occurrence:random_seed=2231566140:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.11/1.11 % (3856914)Also succeeded, but the first one will report.
% 3.11/1.11 % (3856886)Refutation found. Thanks to Tanya!
% 3.11/1.11 % SZS status Theorem for theBenchmark
% 3.11/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.21 % (3856886)------------------------------
% 3.72/1.21 % (3856886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.21 % (3856886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.21 % (3856886)CaDiCaL version: 2.1.3
% 3.72/1.21 % (3856886)Termination reason: Refutation
% 3.72/1.21 % (3856886)Time elapsed: 0.004 s
% 3.72/1.21 % (3856886)Peak memory usage: 89 MB
% 3.72/1.21 % (3856886)Instructions burned: 3 (million)
% 3.72/1.21 % (3856886)------------------------------
% 3.72/1.21 % (3856886)------------------------------
% 3.72/1.21 % (3856818)Success in time 0.448 s
% 3.72/1.21 % Vampire exiting
%------------------------------------------------------------------------------