%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX239_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:46:16 PM UTC 2026
% Result : Theorem 2.17s 1.41s
% Output : Refutation 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 293 ( 9 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 185 ( 79 ~; 73 |; 21 &)
% ( 9 <=>; 1 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 120 ( 120 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 5 prp; 0-4 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 110 ( 0 sgn 106 !; 4 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cons3: ( $o * $i ) > $i ).
tff(func_def_37,type,
bG0: $o > $o ).
tff(func_def_38,type,
bG1: $o > $o ).
tff(func_def_39,type,
bG2: $o > $o ).
tff(func_def_40,type,
bG3: $o > $o ).
tff(func_def_41,type,
bG4: ( $i * $i * $i * $i ) > $o ).
tff(f51,axiom,
eps2(eps),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
tff(f52,axiom,
! [X0: $i,X1: $i] :
( eps2(x(X0,X1))
<=> ( eps2(X0)
| eps2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
tff(f53,axiom,
! [X0: $i,X1: $i] :
( eps2(y(X0,X1))
<=> ( eps2(X0)
& eps2(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
tff(f54,axiom,
! [X0: $i] : eps2(star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
tff(f56,axiom,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
=> ( step(atom(X1),X0) = eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
tff(f61,axiom,
! [X0: $i,X1: $i] : ( step(star(X1),X0) = y(step(X1,X0),star(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
tff(f62,axiom,
! [X0: $i] :
( rec(X0,nil2)
<=> eps2(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
tff(f63,axiom,
! [X0: $i,X1: $i,X2: $i] :
( rec(X0,cons2(X1,X2))
<=> rec(step(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
tff(f67,axiom,
! [X0: $i] : ~ reck2(atom(X0),nil2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
tff(f70,axiom,
! [X0: $i,X1: $i,X2: $i] :
( reck2(x(X1,X2),X0)
<=> ( reck2(X1,X0)
| reck2(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
tff(f73,axiom,
! [X0: $i,X1: $i,X2: $i] :
( reck2(star(X0),cons2(X1,X2))
<=> ( ~ eps2(X0)
& rec(y(X0,star(X0)),cons2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_074) ).
tff(f76,conjecture,
? [X0: $i,X1: $i] :
( rec(X0,X1)
<~> reck2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_077) ).
tff(f77,negated_conjecture,
~ ? [X0: $i,X1: $i] :
( rec(X0,X1)
<~> reck2(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f76]) ).
tff(f107,plain,
! [X0: $i,X1: $i] :
( ( step(atom(X1),X0) = eps )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f56]) ).
tff(f111,plain,
! [X0: $i,X1: $i] :
( rec(X0,X1)
<=> reck2(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
tff(f121,plain,
! [X0: $i,X1: $i] :
( ( eps2(x(X0,X1))
| ( ~ eps2(X0)
& ~ eps2(X1) ) )
& ( eps2(X0)
| eps2(X1)
| ~ eps2(x(X0,X1)) ) ),
inference(nnf_transformation,[],[f52]) ).
tff(f122,plain,
! [X0: $i,X1: $i] :
( ( eps2(x(X0,X1))
| ( ~ eps2(X0)
& ~ eps2(X1) ) )
& ( eps2(X0)
| eps2(X1)
| ~ eps2(x(X0,X1)) ) ),
inference(flattening,[],[f121]) ).
tff(f123,plain,
! [X0: $i,X1: $i] :
( ( eps2(y(X0,X1))
| ~ eps2(X0)
| ~ eps2(X1) )
& ( ( eps2(X0)
& eps2(X1) )
| ~ eps2(y(X0,X1)) ) ),
inference(nnf_transformation,[],[f53]) ).
tff(f124,plain,
! [X0: $i,X1: $i] :
( ( eps2(y(X0,X1))
| ~ eps2(X0)
| ~ eps2(X1) )
& ( ( eps2(X0)
& eps2(X1) )
| ~ eps2(y(X0,X1)) ) ),
inference(flattening,[],[f123]) ).
tff(f125,plain,
! [X0: $i] :
( ( rec(X0,nil2)
| ~ eps2(X0) )
& ( eps2(X0)
| ~ rec(X0,nil2) ) ),
inference(nnf_transformation,[],[f62]) ).
tff(f126,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( rec(X0,cons2(X1,X2))
| ~ rec(step(X0,X1),X2) )
& ( rec(step(X0,X1),X2)
| ~ rec(X0,cons2(X1,X2)) ) ),
inference(nnf_transformation,[],[f63]) ).
tff(f128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( reck2(x(X1,X2),X0)
| ( ~ reck2(X1,X0)
& ~ reck2(X2,X0) ) )
& ( reck2(X1,X0)
| reck2(X2,X0)
| ~ reck2(x(X1,X2),X0) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( reck2(x(X1,X2),X0)
| ( ~ reck2(X1,X0)
& ~ reck2(X2,X0) ) )
& ( reck2(X1,X0)
| reck2(X2,X0)
| ~ reck2(x(X1,X2),X0) ) ),
inference(flattening,[],[f128]) ).
tff(f131,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( reck2(star(X0),cons2(X1,X2))
| eps2(X0)
| ~ rec(y(X0,star(X0)),cons2(X1,X2)) )
& ( ( ~ eps2(X0)
& rec(y(X0,star(X0)),cons2(X1,X2)) )
| ~ reck2(star(X0),cons2(X1,X2)) ) ),
inference(nnf_transformation,[],[f73]) ).
tff(f132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( reck2(star(X0),cons2(X1,X2))
| eps2(X0)
| ~ rec(y(X0,star(X0)),cons2(X1,X2)) )
& ( ( ~ eps2(X0)
& rec(y(X0,star(X0)),cons2(X1,X2)) )
| ~ reck2(star(X0),cons2(X1,X2)) ) ),
inference(flattening,[],[f131]) ).
tff(f133,plain,
! [X0: $i,X1: $i] :
( ( rec(X0,X1)
| ~ reck2(X0,X1) )
& ( reck2(X0,X1)
| ~ rec(X0,X1) ) ),
inference(nnf_transformation,[],[f111]) ).
tff(f198,plain,
eps2(eps),
inference(cnf_transformation,[],[f51]) ).
tff(f201,plain,
! [X0: $i,X1: $i] :
( eps2(x(X0,X1))
| ~ eps2(X0) ),
inference(cnf_transformation,[],[f122]) ).
tff(f204,plain,
! [X0: $i,X1: $i] :
( eps2(y(X0,X1))
| ~ eps2(X0)
| ~ eps2(X1) ),
inference(cnf_transformation,[],[f124]) ).
tff(f205,plain,
! [X0: $i] : eps2(star(X0)),
inference(cnf_transformation,[],[f54]) ).
tff(f207,plain,
! [X0: $i,X1: $i] :
( ( eps = step(atom(X1),X0) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f107]) ).
tff(f212,plain,
! [X0: $i,X1: $i] : ( step(star(X1),X0) = y(step(X1,X0),star(X1)) ),
inference(cnf_transformation,[],[f61]) ).
tff(f214,plain,
! [X0: $i] :
( rec(X0,nil2)
| ~ eps2(X0) ),
inference(cnf_transformation,[],[f125]) ).
tff(f216,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ rec(step(X0,X1),X2)
| rec(X0,cons2(X1,X2)) ),
inference(cnf_transformation,[],[f126]) ).
tff(f220,plain,
! [X0: $i] : ~ reck2(atom(X0),nil2),
inference(cnf_transformation,[],[f67]) ).
tff(f224,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ reck2(x(X1,X2),X0)
| reck2(X2,X0)
| reck2(X1,X0) ),
inference(cnf_transformation,[],[f129]) ).
tff(f231,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ reck2(star(X0),cons2(X1,X2))
| ~ eps2(X0) ),
inference(cnf_transformation,[],[f132]) ).
tff(f235,plain,
! [X0: $i,X1: $i] :
( reck2(X0,X1)
| ~ rec(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tff(f236,plain,
! [X0: $i,X1: $i] :
( rec(X0,X1)
| ~ reck2(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tff(f245,plain,
! [X1: $i] : ( eps = step(atom(X1),X1) ),
inference(equality_resolution,[],[f207]) ).
tff(f259,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ rec(star(X0),cons2(X1,X2))
| ~ eps2(X0) ),
inference(resolution,[],[f231,f235]) ).
tff(f265,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ reck2(step(X0,X1),X2)
| rec(X0,cons2(X1,X2)) ),
inference(resolution,[],[f216,f236]) ).
tff(f270,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ rec(x(X2,X0),X1)
| reck2(X2,X1)
| reck2(X0,X1) ),
inference(resolution,[],[f224,f235]) ).
tff(f272,plain,
! [X0: $i,X1: $i] :
( ~ eps2(x(X0,X1))
| reck2(X1,nil2)
| reck2(X0,nil2) ),
inference(resolution,[],[f270,f214]) ).
tff(f282,definition,
( spl5_1
<=> ! [X1: $i] : reck2(X1,nil2) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f283,plain,
( ! [X1: $i] : reck2(X1,nil2)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f282]) ).
tff(f285,definition,
( spl5_2
<=> ! [X0: $i] :
( ~ eps2(X0)
| reck2(X0,nil2) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f286,plain,
( ! [X0: $i] :
( reck2(X0,nil2)
| ~ eps2(X0) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f285]) ).
tff(f288,plain,
! [X0: $i,X1: $i] :
( ~ eps2(X0)
| reck2(X1,nil2)
| reck2(X0,nil2) ),
inference(resolution,[],[f201,f272]) ).
tff(f289,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f288,f285,f282]) ).
tff(f293,plain,
( ! [X0: $i,X1: $i] :
( ~ eps2(step(X0,X1))
| rec(X0,cons2(X1,nil2)) )
| ~ spl5_2 ),
inference(resolution,[],[f286,f265]) ).
tff(f661,plain,
! [X0: $i,X1: $i] :
( eps2(step(star(X0),X1))
| ~ eps2(step(X0,X1))
| ~ eps2(star(X0)) ),
inference(superposition,[],[f204,f212]) ).
tff(f663,plain,
! [X0: $i,X1: $i] :
( eps2(step(star(X0),X1))
| ~ eps2(step(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f661,f205]) ).
tff(f883,plain,
( ! [X0: $i,X1: $i] :
( rec(star(X0),cons2(X1,nil2))
| ~ eps2(step(X0,X1)) )
| ~ spl5_2 ),
inference(resolution,[],[f663,f293]) ).
tff(f923,plain,
( ! [X0: $i,X1: $i] :
( ~ eps2(step(X0,X1))
| ~ eps2(X0) )
| ~ spl5_2 ),
inference(resolution,[],[f883,f259]) ).
tff(f926,plain,
( ! [X0: $i,X1: $i] :
( ~ eps2(star(X0))
| ~ eps2(step(X0,X1)) )
| ~ spl5_2 ),
inference(resolution,[],[f923,f663]) ).
tff(f931,plain,
( ! [X0: $i,X1: $i] : ~ eps2(step(X0,X1))
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f926,f205]) ).
tff(f941,plain,
( ~ eps2(eps)
| ~ spl5_2 ),
inference(superposition,[],[f931,f245]) ).
tff(f943,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f941,f198]) ).
tff(f944,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f943]) ).
tff(f953,plain,
( $false
| ~ spl5_1 ),
inference(resolution,[],[f283,f220]) ).
tff(f962,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f953]) ).
cnf(s2,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f289]) ).
cnf(s21,plain,
~ spl5_2,
inference(sat_conversion,[],[f944]) ).
cnf(s23,plain,
~ spl5_1,
inference(sat_conversion,[],[f962]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s2,s21,s23]) ).
tff(f966,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX239_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n001.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.22/0.27 % CPULimit : 300
% 0.22/0.27 % WCLimit : 300
% 0.22/0.27 % DateTime : Mon Sep 28 15:23:33 UTC 2026
% 0.22/0.27 % CPUTime :
% 0.22/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.32 Running first-order theorem proving
% 0.22/0.32 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
% 2.17/1.41 % (426253)Detected formulas, will run a generic FOF schedule.
% 2.17/1.41 % (426265)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4177786556:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.17/1.41 % (426262)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=3383740294:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.17/1.41 % (426265)First to succeed.
% 2.17/1.41 % (426265)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-426253"
% 2.17/1.41 % (426260)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=109767736:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.17/1.41 % (426261)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=1121764596:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.17/1.41 % (426263)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2829182559:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.17/1.41 % (426266)dis-21_1_sil=8000:lcm=predicate:random_seed=3879443558: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)
% 2.17/1.41 % (426264)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=176499580:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.17/1.41 % (426264)Also succeeded, but the first one will report.
% 2.17/1.41 % (426263)Instruction limit reached!
% 2.17/1.41 % (426263)------------------------------
% 2.17/1.41 % (426263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.41 % (426263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.41 % (426263)CaDiCaL version: 2.1.3
% 2.17/1.41 % (426263)Termination reason: Instruction limit
% 2.17/1.41 % (426263)Termination phase: Saturation
% 2.17/1.41 % (426263)Time elapsed: 0.094 s
% 2.17/1.41 % (426263)Peak memory usage: 89 MB
% 2.17/1.41 % (426263)Instructions burned: 109 (million)
% 2.17/1.41 % (426266)Instruction limit reached!
% 2.17/1.41 % (426266)------------------------------
% 2.17/1.41 % (426266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.17/1.41 % (426266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.17/1.41 % (426266)CaDiCaL version: 2.1.3
% 2.17/1.41 % (426266)Termination reason: Instruction limit
% 2.17/1.41 % (426266)Termination phase: Saturation
% 2.17/1.41 % (426266)Time elapsed: 0.121 s
% 2.17/1.41 % (426266)Peak memory usage: 90 MB
% 2.17/1.41 % (426266)Instructions burned: 129 (million)
% 2.17/1.41 % (426265)Refutation found. Thanks to Tanya!
% 2.17/1.41 % SZS status Theorem for theBenchmark
% 2.17/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 4.23/1.70 % (426265)------------------------------
% 4.23/1.70 % (426265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.23/1.70 % (426265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.23/1.70 % (426265)CaDiCaL version: 2.1.3
% 4.23/1.70 % (426265)Termination reason: Refutation
% 4.23/1.70 % (426265)Time elapsed: 0.024 s
% 4.23/1.70 % (426265)Peak memory usage: 90 MB
% 4.23/1.70 % (426265)Instructions burned: 34 (million)
% 4.23/1.70 % (426265)------------------------------
% 4.23/1.70 % (426265)------------------------------
% 4.23/1.70 % (426253)Success in time 0.451 s
% 4.23/1.70 % Vampire exiting
%------------------------------------------------------------------------------