%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:46:13 PM UTC 2026
% Result : Theorem 4.30s 1.48s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 18 unt; 1 def)
% Number of atoms : 87 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 39 ~; 31 |; 7 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 0 sgn 106 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(f26,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0,X1,X2,X3,X4] :
( tc(X0,app(X2,X3,X4),X1)
<=> ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1,X2,X3] :
( tc(X0,lam(X1),arr(X2,X3))
<=> tc(cons(X2,X0),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( index(X0,X2) = just(X3)
=> ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(f32,conjecture,
? [X0] : tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
fof(f33,negated_conjecture,
~ ? [X0] : tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,var(X2),X1)
<=> X3 = X1 )
| index(X0,X2) != just(X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(ennf_transformation,[],[f33]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4] :
( ( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) )
& ( ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) )
| ~ tc(X0,app(X2,X3,X4),X1) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4] :
( ( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) )
& ( ( tc(X0,X2,arr(X4,X1))
& tc(X0,X3,X4) )
| ~ tc(X0,app(X2,X3,X4),X1) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) )
& ( tc(cons(X2,X0),X1,X3)
| ~ tc(X0,lam(X1),arr(X2,X3)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ( ( tc(X0,var(X2),X1)
| X1 != X3 )
& ( X3 = X1
| ~ tc(X0,var(X2),X1) ) )
| index(X0,X2) != just(X3) ),
inference(nnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f25]) ).
fof(f67,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f26]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(X0,X2,arr(X4,X1))
| tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X3,X4) ),
inference(cnf_transformation,[],[f39]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( tc(X0,var(X2),X1)
| X1 != X3
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[],[f41]) ).
fof(f77,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(cnf_transformation,[],[f37]) ).
fof(f78,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f76]) ).
fof(f80,plain,
! [X2,X0,X1] :
( just(X0) != just(X2)
| tc(cons(X0,X1),var(zero),X2) ),
inference(superposition,[],[f78,f66]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( just(X3) != index(X0,X1)
| tc(cons(X2,X0),var(suc(X1)),X3) ),
inference(superposition,[],[f78,f67]) ).
fof(f82,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[],[f80]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( just(X0) != just(X1)
| tc(cons(X3,cons(X0,X2)),var(suc(zero)),X1) ),
inference(superposition,[],[f81,f66]) ).
fof(f86,plain,
! [X0,X1] : tc(X0,lam(var(zero)),arr(X1,X1)),
inference(resolution,[],[f82,f73]) ).
fof(f92,plain,
! [X2,X0,X1] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[],[f84]) ).
fof(f95,plain,
! [X2,X0,X1] :
( tc(X0,app(lam(var(zero)),X1,X2),X2)
| ~ tc(X0,X1,X2) ),
inference(resolution,[],[f86,f70]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X4] :
( tc(cons(X0,cons(arr(X1,X2),X3)),app(var(suc(zero)),X4,X1),X2)
| ~ tc(cons(X0,cons(arr(X1,X2),X3)),X4,X1) ),
inference(resolution,[],[f92,f70]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( tc(X1,lam(app(lam(var(zero)),X2,X3)),arr(X0,X3))
| ~ tc(cons(X0,X1),X2,X3) ),
inference(resolution,[],[f95,f73]) ).
fof(f196,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( tc(cons(X0,cons(arr(X1,arr(X2,X3)),X4)),app(app(var(suc(zero)),X5,X1),X6,X2),X3)
| ~ tc(cons(X0,cons(arr(X1,arr(X2,X3)),X4)),X5,X1)
| ~ tc(cons(X0,cons(arr(X1,arr(X2,X3)),X4)),X6,X2) ),
inference(resolution,[],[f105,f70]) ).
fof(f231,plain,
! [X0] : ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b)),
inference(resolution,[],[f137,f77]) ).
fof(f259,plain,
! [X0] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b),
inference(resolution,[],[f231,f137]) ).
fof(f366,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a) ),
inference(resolution,[],[f196,f259]) ).
fof(f373,definition,
( spl0_1
<=> ! [X1] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f374,plain,
( ! [X1] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( spl0_1
| spl0_1 ),
inference(avatar_split_clause,[],[f366,f373,f373]) ).
fof(f411,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f374,f82]) ).
fof(f415,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f411]) ).
cnf(s1,plain,
( spl0_1
| spl0_1 ),
inference(sat_conversion,[],[f375]) ).
cnf(s2,plain,
spl0_1,
inference(rat,[],[s1]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f415]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f416,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 % Computer : n007.cluster.edu
% 0.26/0.28 % Model : x86_64 x86_64
% 0.26/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.28 % Memory : 8046.5625MB
% 0.26/0.28 % OS : Linux 6.8.0-71-generic
% 0.26/0.28 % CPULimit : 300
% 0.26/0.28 % WCLimit : 300
% 0.26/0.28 % DateTime : Mon Sep 28 15:11:10 UTC 2026
% 0.26/0.29 % CPUTime :
% 0.26/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.35 Running first-order theorem proving
% 0.26/0.35 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
% 4.30/1.48 % (2487786)Detected formulas, will run a generic FOF schedule.
% 4.30/1.48 % (2487796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1514424579:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.30/1.48 % (2487793)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=2780415982:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.30/1.48 % (2487795)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2580405638:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.30/1.48 % (2487794)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1049059394:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.30/1.48 % (2487792)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=1249342229:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.30/1.48 % (2487791)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=1478293522:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.30/1.48 % (2487796)First to succeed.
% 4.30/1.48 % (2487796)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2487786"
% 4.30/1.48 % (2487797)dis-21_1_sil=8000:lcm=predicate:random_seed=3274910401: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)
% 4.30/1.48 % (2487794)Instruction limit reached!
% 4.30/1.48 % (2487794)------------------------------
% 4.30/1.48 % (2487794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.48 % (2487794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.48 % (2487794)CaDiCaL version: 2.1.3
% 4.30/1.48 % (2487794)Termination reason: Instruction limit
% 4.30/1.48 % (2487794)Termination phase: Saturation
% 4.30/1.48 % (2487794)Time elapsed: 0.085 s
% 4.30/1.48 % (2487794)Peak memory usage: 88 MB
% 4.30/1.48 % (2487794)Instructions burned: 110 (million)
% 4.30/1.48 % (2487795)Instruction limit reached!
% 4.30/1.48 % (2487795)------------------------------
% 4.30/1.48 % (2487795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.48 % (2487795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.48 % (2487795)CaDiCaL version: 2.1.3
% 4.30/1.48 % (2487795)Termination reason: Instruction limit
% 4.30/1.48 % (2487795)Termination phase: Saturation
% 4.30/1.48 % (2487795)Time elapsed: 0.109 s
% 4.30/1.48 % (2487795)Peak memory usage: 88 MB
% 4.30/1.48 % (2487795)Instructions burned: 120 (million)
% 4.30/1.48 % (2487797)Instruction limit reached!
% 4.30/1.48 % (2487797)------------------------------
% 4.30/1.48 % (2487797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.48 % (2487797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.48 % (2487797)CaDiCaL version: 2.1.3
% 4.30/1.48 % (2487797)Termination reason: Instruction limit
% 4.30/1.48 % (2487797)Termination phase: Saturation
% 4.30/1.48 % (2487797)Time elapsed: 0.132 s
% 4.30/1.48 % (2487797)Peak memory usage: 89 MB
% 4.30/1.48 % (2487797)Instructions burned: 129 (million)
% 4.30/1.48 % (2487796)Refutation found. Thanks to Tanya!
% 4.30/1.48 % SZS status Theorem for theBenchmark
% 4.30/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 4.30/1.48 % (2487796)------------------------------
% 4.30/1.48 % (2487796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.48 % (2487796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.48 % (2487796)CaDiCaL version: 2.1.3
% 4.30/1.48 % (2487796)Termination reason: Refutation
% 4.30/1.48 % (2487796)Time elapsed: 0.017 s
% 4.30/1.48 % (2487796)Peak memory usage: 90 MB
% 4.30/1.48 % (2487796)Instructions burned: 26 (million)
% 4.30/1.48 % (2487796)------------------------------
% 4.30/1.48 % (2487796)------------------------------
% 4.30/1.48 % (2487786)Success in time 0.51 s
% 4.30/1.48 % Vampire exiting
%------------------------------------------------------------------------------