%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CSR018+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 09:44:21 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 25 unt; 6 def)
% Number of atoms : 301 ( 111 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 327 ( 117 ~; 128 |; 67 &)
% ( 14 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 104 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1,X2] :
( ( happens(X0,X1)
& initiates(X0,X2,X1) )
=> holdsAt(X2,plus(X1,n1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+0.ax',happens_holds) ).
fof(f13,axiom,
! [X0,X1,X2] :
( initiates(X0,X1,X2)
<=> ( ( X0 = push
& X1 = forwards
& ~ happens(pull,X2) )
| ( X0 = pull
& X1 = backwards
& ~ happens(push,X2) )
| ( X0 = pull
& X1 = spinning
& happens(push,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',initiates_all_defn) ).
fof(f16,axiom,
! [X0,X1] :
( happens(X0,X1)
<=> ( ( X0 = push
& X1 = n0 )
| ( X0 = pull
& X1 = n1 )
| ( X0 = pull
& X1 = n2 )
| ( X0 = push
& X1 = n2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',happens_all_defn) ).
fof(f17,axiom,
push != pull,
file('/export/starexec/sandbox2/benchmark/Axioms/CSR001+2.ax',push_not_pull) ).
fof(f25,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_1) ).
fof(f32,axiom,
! [X0,X1] :
( less_or_equal(X0,X1)
<=> ( less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal) ).
fof(f33,axiom,
~ ? [X0] : less(X0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less0) ).
fof(f34,axiom,
! [X0] :
( less(X0,n1)
<=> less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less1) ).
fof(f35,axiom,
! [X0] :
( less(X0,n2)
<=> less_or_equal(X0,n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less2) ).
fof(f43,axiom,
! [X0,X1] :
( less(X0,X1)
<=> ( ~ less(X1,X0)
& X1 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
fof(f48,conjecture,
holdsAt(backwards,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backwards_2) ).
fof(f49,negated_conjecture,
~ holdsAt(backwards,n2),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,plain,
~ holdsAt(backwards,n2),
inference(flattening,[],[f49]) ).
fof(f65,plain,
! [X0,X1,X2] :
( holdsAt(X2,plus(X1,n1))
| ~ happens(X0,X1)
| ~ initiates(X0,X2,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1,X2] :
( holdsAt(X2,plus(X1,n1))
| ~ happens(X0,X1)
| ~ initiates(X0,X2,X1) ),
inference(flattening,[],[f65]) ).
fof(f73,plain,
! [X0] : ~ less(X0,n0),
inference(ennf_transformation,[],[f33]) ).
fof(f74,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ( X0 = pull
& X1 = spinning
& happens(push,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f75,definition,
! [X0,X1,X2] :
( sP1(X0,X1,X2)
<=> ( X0 = pull
& X1 = backwards
& ~ happens(push,X2) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f76,plain,
! [X0,X1,X2] :
( initiates(X0,X1,X2)
<=> ( ( X0 = push
& X1 = forwards
& ~ happens(pull,X2) )
| sP1(X0,X1,X2)
| sP0(X0,X1,X2) ) ),
inference(definition_folding,[],[f13,f75,f74]) ).
fof(f84,definition,
! [X0,X1] :
( sP8(X0,X1)
<=> ( X0 = push
& X1 = n2 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f85,definition,
! [X0,X1] :
( sP9(X0,X1)
<=> ( ( X0 = push
& X1 = n0 )
| ( X0 = pull
& X1 = n1 )
| ( X0 = pull
& X1 = n2 )
| sP8(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f86,plain,
! [X0,X1] :
( happens(X0,X1)
<=> sP9(X0,X1) ),
inference(definition_folding,[],[f16,f85,f84]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| pull != X0
| backwards != X1
| happens(push,X2) )
& ( ( X0 = pull
& X1 = backwards
& ~ happens(push,X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| pull != X0
| backwards != X1
| happens(push,X2) )
& ( ( X0 = pull
& X1 = backwards
& ~ happens(push,X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(flattening,[],[f91]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( initiates(X0,X1,X2)
| ( ( push != X0
| forwards != X1
| happens(pull,X2) )
& ~ sP1(X0,X1,X2)
& ~ sP0(X0,X1,X2) ) )
& ( ( X0 = push
& X1 = forwards
& ~ happens(pull,X2) )
| sP1(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ initiates(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( initiates(X0,X1,X2)
| ( ( push != X0
| forwards != X1
| happens(pull,X2) )
& ~ sP1(X0,X1,X2)
& ~ sP0(X0,X1,X2) ) )
& ( ( X0 = push
& X1 = forwards
& ~ happens(pull,X2) )
| sP1(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ initiates(X0,X1,X2) ) ),
inference(flattening,[],[f95]) ).
fof(f110,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ( push != X0
| n0 != X1 )
& ( pull != X0
| n1 != X1 )
& ( pull != X0
| n2 != X1 )
& ~ sP8(X0,X1) ) )
& ( ( X0 = push
& X1 = n0 )
| ( X0 = pull
& X1 = n1 )
| ( X0 = pull
& X1 = n2 )
| sP8(X0,X1)
| ~ sP9(X0,X1) ) ),
inference(nnf_transformation,[],[f85]) ).
fof(f111,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ( push != X0
| n0 != X1 )
& ( pull != X0
| n1 != X1 )
& ( pull != X0
| n2 != X1 )
& ~ sP8(X0,X1) ) )
& ( ( X0 = push
& X1 = n0 )
| ( X0 = pull
& X1 = n1 )
| ( X0 = pull
& X1 = n2 )
| sP8(X0,X1)
| ~ sP9(X0,X1) ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| push != X0
| n2 != X1 )
& ( ( X0 = push
& X1 = n2 )
| ~ sP8(X0,X1) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f113,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| push != X0
| n2 != X1 )
& ( ( X0 = push
& X1 = n2 )
| ~ sP8(X0,X1) ) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( ( happens(X0,X1)
| ~ sP9(X0,X1) )
& ( sP9(X0,X1)
| ~ happens(X0,X1) ) ),
inference(nnf_transformation,[],[f86]) ).
fof(f115,plain,
! [X0,X1] :
( ( less_or_equal(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ less_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f116,plain,
! [X0,X1] :
( ( less_or_equal(X0,X1)
| ( ~ less(X0,X1)
& X0 != X1 ) )
& ( less(X0,X1)
| X0 = X1
| ~ less_or_equal(X0,X1) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0] :
( ( less(X0,n1)
| ~ less_or_equal(X0,n0) )
& ( less_or_equal(X0,n0)
| ~ less(X0,n1) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f118,plain,
! [X0] :
( ( less(X0,n2)
| ~ less_or_equal(X0,n1) )
& ( less_or_equal(X0,n1)
| ~ less(X0,n2) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f126,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f127,plain,
! [X0,X1] :
( ( less(X0,X1)
| less(X1,X0)
| X0 = X1 )
& ( ( ~ less(X1,X0)
& X1 != X0 )
| ~ less(X0,X1) ) ),
inference(flattening,[],[f126]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ initiates(X0,X2,X1)
| ~ happens(X0,X1)
| holdsAt(X2,plus(X1,n1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| pull != X0
| backwards != X1
| happens(push,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| initiates(X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f190,plain,
! [X0,X1] :
( n0 = X1
| pull = X0
| pull = X0
| sP8(X0,X1)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f197,plain,
! [X0,X1] :
( sP9(X0,X1)
| pull != X0
| n1 != X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f199,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| n2 = X1 ),
inference(cnf_transformation,[],[f113]) ).
fof(f202,plain,
! [X0,X1] :
( ~ happens(X0,X1)
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f203,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| happens(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f204,plain,
push != pull,
inference(cnf_transformation,[],[f17]) ).
fof(f212,plain,
n2 = plus(n1,n1),
inference(cnf_transformation,[],[f25]) ).
fof(f220,plain,
! [X0,X1] :
( less_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f116]) ).
fof(f222,plain,
! [X0] : ~ less(X0,n0),
inference(cnf_transformation,[],[f73]) ).
fof(f224,plain,
! [X0] :
( ~ less_or_equal(X0,n0)
| less(X0,n1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f226,plain,
! [X0] :
( ~ less_or_equal(X0,n1)
| less(X0,n2) ),
inference(cnf_transformation,[],[f118]) ).
fof(f241,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f248,plain,
~ holdsAt(backwards,n2),
inference(cnf_transformation,[],[f50]) ).
fof(f249,plain,
! [X2,X1] :
( sP1(pull,X1,X2)
| backwards != X1
| happens(push,X2) ),
inference(equality_resolution,[],[f144]) ).
fof(f250,plain,
! [X2] :
( sP1(pull,backwards,X2)
| happens(push,X2) ),
inference(equality_resolution,[],[f249]) ).
fof(f269,plain,
! [X1] :
( sP9(pull,X1)
| n1 != X1 ),
inference(equality_resolution,[],[f197]) ).
fof(f270,plain,
sP9(pull,n1),
inference(equality_resolution,[],[f269]) ).
fof(f275,plain,
! [X1] : less_or_equal(X1,X1),
inference(equality_resolution,[],[f220]) ).
fof(f276,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f241]) ).
fof(f277,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| pull = X0
| sP8(X0,X1)
| n0 = X1 ),
inference(duplicate_literal_removal,[],[f190]) ).
fof(f284,plain,
happens(pull,n1),
inference(resolution,[],[f203,f270]) ).
fof(f288,plain,
less(n0,n1),
inference(resolution,[],[f224,f275]) ).
fof(f292,plain,
less(n1,n2),
inference(resolution,[],[f226,f275]) ).
fof(f387,plain,
! [X0] :
( initiates(pull,backwards,X0)
| happens(push,X0) ),
inference(resolution,[],[f153,f250]) ).
fof(f703,plain,
! [X0] :
( holdsAt(backwards,plus(X0,n1))
| ~ happens(pull,X0)
| happens(push,X0) ),
inference(resolution,[],[f387,f136]) ).
fof(f883,definition,
( spl14_11
<=> n0 = n1 ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
fof(f884,plain,
( n0 != n1
| spl14_11 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f885,plain,
( n0 = n1
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f929,definition,
( spl14_13
<=> happens(push,n1) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
fof(f931,plain,
( happens(push,n1)
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f1269,plain,
( less(n0,n0)
| ~ spl14_11 ),
inference(superposition,[],[f288,f885]) ).
fof(f1315,plain,
( $false
| ~ spl14_11 ),
inference(forward_subsumption_resolution,[],[f1269,f222]) ).
fof(f1316,plain,
~ spl14_11,
inference(avatar_contradiction_clause,[],[f1315]) ).
fof(f1392,plain,
( holdsAt(backwards,n2)
| ~ happens(pull,n1)
| happens(push,n1) ),
inference(superposition,[],[f703,f212]) ).
fof(f1393,plain,
( ~ happens(pull,n1)
| happens(push,n1) ),
inference(forward_subsumption_resolution,[],[f1392,f248]) ).
fof(f1396,plain,
happens(push,n1),
inference(forward_subsumption_resolution,[],[f1393,f284]) ).
fof(f1407,plain,
spl14_13,
inference(avatar_split_clause,[],[f1396,f929]) ).
fof(f1424,plain,
( sP9(push,n1)
| ~ spl14_13 ),
inference(resolution,[],[f931,f202]) ).
fof(f1428,plain,
( push = pull
| sP8(push,n1)
| n0 = n1
| ~ spl14_13 ),
inference(resolution,[],[f1424,f277]) ).
fof(f1430,plain,
( sP8(push,n1)
| n0 = n1
| ~ spl14_13 ),
inference(forward_subsumption_resolution,[],[f1428,f204]) ).
fof(f1431,plain,
( sP8(push,n1)
| spl14_11
| ~ spl14_13 ),
inference(forward_subsumption_resolution,[],[f1430,f884]) ).
fof(f1454,plain,
( n1 = n2
| spl14_11
| ~ spl14_13 ),
inference(resolution,[],[f1431,f199]) ).
fof(f1488,plain,
( less(n1,n1)
| spl14_11
| ~ spl14_13 ),
inference(superposition,[],[f292,f1454]) ).
fof(f1530,plain,
( $false
| spl14_11
| ~ spl14_13 ),
inference(forward_subsumption_resolution,[],[f1488,f276]) ).
fof(f1531,plain,
( spl14_11
| ~ spl14_13 ),
inference(avatar_contradiction_clause,[],[f1530]) ).
cnf(s31,plain,
~ spl14_11,
inference(sat_conversion,[],[f1316]) ).
cnf(s39,plain,
spl14_13,
inference(sat_conversion,[],[f1407]) ).
cnf(s44,plain,
( spl14_11
| ~ spl14_13 ),
inference(sat_conversion,[],[f1531]) ).
cnf(s45,plain,
spl14_11,
inference(rat,[],[s44,s39]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s31,s45]) ).
fof(f1537,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CSR018+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n018.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 22:07:56 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.26 % (3846355)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (3846363)dis+10_1_sil=32000:sp=arity:random_seed=4211532989:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (3846361)% WARNING: option uhcvi not known.
% 0.19/0.26 % (3846360)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=90578914_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (3846361)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3073249903:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (3846362)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2707910659:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (3846364)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2827530266:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (3846365)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=108908580:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.26 % (3846366)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2246569132:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.26 % Detected minimum model sizes of [3]
% 0.19/0.26 % Detected maximum model sizes of [max]
% 0.19/0.26 % TRYING [3]
% 0.19/0.26 % (3846363) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3846355-3846363"...
% 0.19/0.26 % (3846363)...printing done.
% 0.19/0.26 % (3846363)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3846363)------------------------------
% 0.19/0.27 % (3846363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3846363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3846363)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3846363)Termination reason: Refutation
% 0.19/0.27 % (3846363)Time elapsed: 0.016 s
% 0.19/0.27 % (3846363)Peak memory usage: 13 MB
% 0.19/0.27 % (3846363)Instructions burned: 44 (million)
% 0.19/0.27 % (3846355)Success in time 0.041 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------