%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX220+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 : n013.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 01:46:12 PM UTC 2026
% Result : Theorem 3.78s 1.27s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 20 unt; 2 def)
% Number of atoms : 95 ( 19 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 95 ( 48 ~; 33 |; 7 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 110 !; 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(b,c)),arr(b,arr(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_032) ).
fof(f33,negated_conjecture,
~ ? [X0] : tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(ennf_transformation,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,var(X2),X1)
<=> X3 = X1 )
| index(X0,X2) != just(X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f38,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,[],[f35]) ).
fof(f39,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(f40,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(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(cnf_transformation,[],[f34]) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( tc(X0,var(X2),X1)
| X1 != X3
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[],[f38]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) ),
inference(cnf_transformation,[],[f39]) ).
fof(f51,plain,
! [X2,X3,X0,X1,X4] :
( tc(X0,app(X2,X3,X4),X1)
| ~ tc(X0,X2,arr(X4,X1))
| ~ tc(X0,X3,X4) ),
inference(cnf_transformation,[],[f41]) ).
fof(f60,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f25]) ).
fof(f66,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f26]) ).
fof(f78,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f44]) ).
fof(f84,plain,
! [X2,X0,X1] :
( just(X0) != just(X2)
| tc(cons(X0,X1),var(zero),X2) ),
inference(superposition,[],[f78,f60]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( just(X3) != index(X0,X1)
| tc(cons(X2,X0),var(suc(X1)),X3) ),
inference(superposition,[],[f78,f66]) ).
fof(f86,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[],[f84]) ).
fof(f87,plain,
! [X0] : ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))),
inference(resolution,[],[f47,f42]) ).
fof(f91,plain,
! [X0] : ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c)),
inference(resolution,[],[f87,f47]) ).
fof(f92,plain,
! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c),
inference(resolution,[],[f91,f47]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X1,c))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,X1) ),
inference(resolution,[],[f51,f92]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( just(X0) != just(X1)
| tc(cons(X3,cons(X0,X2)),var(suc(zero)),X1) ),
inference(superposition,[],[f85,f60]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( index(X0,X1) != just(X2)
| tc(cons(X4,cons(X3,X0)),var(suc(suc(X1))),X2) ),
inference(superposition,[],[f85,f66]) ).
fof(f134,plain,
! [X2,X0,X1] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[],[f112]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( just(X0) != just(X2)
| tc(cons(X3,cons(X4,cons(X0,X1))),var(suc(suc(zero))),X2) ),
inference(superposition,[],[f113,f60]) ).
fof(f193,plain,
! [X2,X3,X0,X1] : tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(equality_resolution,[],[f145]) ).
fof(f215,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,arr(X3,arr(X1,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X3) ),
inference(resolution,[],[f101,f51]) ).
fof(f424,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a) ),
inference(resolution,[],[f215,f193]) ).
fof(f428,definition,
( spl0_3
<=> ! [X1] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f429,plain,
( ! [X1] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f431,definition,
( spl0_4
<=> ! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f432,plain,
( ! [X0] : ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f433,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f424,f431,f428]) ).
fof(f434,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f429,f86]) ).
fof(f436,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f440,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f432,f134]) ).
fof(f442,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f440]) ).
cnf(s3,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f433]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f436]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f442]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5,s4]) ).
fof(f443,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX220+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:12:21 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 3.58/1.15 % (1258326)Detected formulas, will run a generic FOF schedule.
% 3.58/1.15 % (1258465)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=200539868:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.15 % (1258465)Instruction limit reached!
% 3.58/1.15 % (1258465)------------------------------
% 3.58/1.15 % (1258465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.15 % (1258465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.15 % (1258465)CaDiCaL version: 2.1.3
% 3.58/1.15 % (1258465)Termination reason: Instruction limit
% 3.58/1.15 % (1258465)Termination phase: Saturation
% 3.58/1.15 % (1258465)Time elapsed: 0.036 s
% 3.58/1.15 % (1258465)Peak memory usage: 88 MB
% 3.58/1.15 % (1258465)Instructions burned: 120 (million)
% 3.58/1.15 % (1258466)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=379296627:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.15 % (1258464)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=391777384:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.15 % (1258463)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=2337961281:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.15 % (1258460)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=3003917350:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.15 % (1258467)dis-21_1_sil=8000:lcm=predicate:random_seed=1686357629: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)
% 3.58/1.15 % (1258464)Instruction limit reached!
% 3.58/1.15 % (1258464)------------------------------
% 3.58/1.15 % (1258464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.15 % (1258464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.15 % (1258464)CaDiCaL version: 2.1.3
% 3.58/1.15 % (1258464)Termination reason: Instruction limit
% 3.58/1.15 % (1258464)Termination phase: Saturation
% 3.58/1.15 % (1258464)Time elapsed: 0.046 s
% 3.58/1.15 % (1258464)Peak memory usage: 88 MB
% 3.58/1.15 % (1258464)Instructions burned: 112 (million)
% 3.58/1.15 % (1258462)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=4293601993:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.15 % (1258467)Instruction limit reached!
% 3.58/1.15 % (1258467)------------------------------
% 3.58/1.15 % (1258467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.15 % (1258467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.15 % (1258467)CaDiCaL version: 2.1.3
% 3.58/1.15 % (1258467)Termination reason: Instruction limit
% 3.58/1.15 % (1258467)Termination phase: Saturation
% 3.58/1.15 % (1258467)Time elapsed: 0.082 s
% 3.58/1.15 % (1258467)Peak memory usage: 89 MB
% 3.58/1.15 % (1258467)Instructions burned: 130 (million)
% 3.58/1.15 % (1258466)Instruction limit reached!
% 3.58/1.15 % (1258466)------------------------------
% 3.58/1.15 % (1258466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.15 % (1258466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.15 % (1258466)CaDiCaL version: 2.1.3
% 3.58/1.15 % (1258466)Termination reason: Instruction limit
% 3.58/1.15 % (1258466)Termination phase: Saturation
% 3.58/1.15 % (1258466)Time elapsed: 0.092 s
% 3.58/1.15 % (1258466)Peak memory usage: 89 MB
% 3.58/1.15 % (1258466)Instructions burned: 140 (million)
% 3.58/1.15 % (1258473)lrs+10_1_sil=8000:sp=occurrence:random_seed=1414394322:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.58/1.15 % (1258473)First to succeed.
% 3.58/1.15 % (1258473)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1258326"
% 3.58/1.15 % (1258476)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2533945657:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.58/1.15 % (1258477)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1400812310:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.58/1.15 % (1258478)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2266205784:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.78/1.27 % (1258477)Refutation not found, incomplete strategy
% 3.78/1.27 % (1258477)------------------------------
% 3.78/1.27 % (1258477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.27 % (1258477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.27 % (1258477)CaDiCaL version: 2.1.3
% 3.78/1.27 % (1258477)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.27 % (1258477)Time elapsed: 0.002 s
% 3.78/1.27 % (1258477)Peak memory usage: 88 MB
% 3.78/1.27 % (1258477)Instructions burned: 1 (million)
% 3.78/1.27 % (1258476)Instruction limit reached!
% 3.78/1.27 % (1258476)------------------------------
% 3.78/1.27 % (1258476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.27 % (1258476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.27 % (1258476)CaDiCaL version: 2.1.3
% 3.78/1.27 % (1258476)Termination reason: Instruction limit
% 3.78/1.27 % (1258476)Termination phase: Saturation
% 3.78/1.27 % (1258476)Time elapsed: 0.098 s
% 3.78/1.27 % (1258476)Peak memory usage: 90 MB
% 3.78/1.27 % (1258476)Instructions burned: 159 (million)
% 3.78/1.27 % (1258473)Refutation found. Thanks to Tanya!
% 3.78/1.27 % SZS status Theorem for theBenchmark
% 3.78/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.27 % (1258473)------------------------------
% 3.78/1.27 % (1258473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.27 % (1258473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.27 % (1258473)CaDiCaL version: 2.1.3
% 3.78/1.27 % (1258473)Termination reason: Refutation
% 3.78/1.27 % (1258473)Time elapsed: 0.015 s
% 3.78/1.27 % (1258473)Peak memory usage: 90 MB
% 3.78/1.27 % (1258473)Instructions burned: 39 (million)
% 3.78/1.27 % (1258473)------------------------------
% 3.78/1.27 % (1258473)------------------------------
% 3.78/1.27 % (1258326)Success in time 0.464 s
% 3.78/1.27 % Vampire exiting
%------------------------------------------------------------------------------