%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX223+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 : n002.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 3.61s 1.23s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 17 unt; 0 def)
% Number of atoms : 135 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 149 ( 69 ~; 55 |; 16 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 127 ( 125 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1,X2,X3] : app(X0,X1,X2) != lam(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(f23,axiom,
! [X0,X1] : lam(X0) != var(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(f24,axiom,
! [X0,X1,X2] :
( X0 != lam(proj1Lam(X0))
=> ( nf(app(X0,X1,X2))
<=> ( nf(X0)
& nf(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f26,axiom,
! [X0] :
( nf(lam(X0))
<=> nf(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0] : nf(var(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(f30,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
fof(f31,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_031) ).
fof(f33,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_033) ).
fof(f35,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_035) ).
fof(f36,conjecture,
? [X0] :
( nf(X0)
& tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(f37,negated_conjecture,
~ ? [X0] :
( nf(X0)
& tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ nf(X0)
| ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))) ),
inference(ennf_transformation,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( nf(app(X0,X1,X2))
<=> ( nf(X0)
& nf(X1) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(ennf_transformation,[],[f24]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ( tc(X0,var(X2),X1)
<=> X3 = X1 )
| index(X0,X2) != just(X3) ),
inference(ennf_transformation,[],[f35]) ).
fof(f43,plain,
! [X0] :
( ( nf(lam(X0))
| ~ nf(X0) )
& ( nf(X0)
| ~ nf(lam(X0)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1) )
& ( ( nf(X0)
& nf(X1) )
| ~ nf(app(X0,X1,X2)) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(nnf_transformation,[],[f39]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1) )
& ( ( nf(X0)
& nf(X1) )
| ~ nf(app(X0,X1,X2)) ) )
| lam(proj1Lam(X0)) = X0 ),
inference(flattening,[],[f44]) ).
fof(f46,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,[],[f40]) ).
fof(f47,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,[],[f33]) ).
fof(f48,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,[],[f31]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b)))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
! [X0] : nf(var(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f53,plain,
! [X0] :
( nf(lam(X0))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X2,X0,X1] :
( nf(app(X0,X1,X2))
| ~ nf(X0)
| ~ nf(X1)
| lam(proj1Lam(X0)) = X0 ),
inference(cnf_transformation,[],[f45]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( tc(X0,var(X2),X1)
| X1 != X3
| index(X0,X2) != just(X3) ),
inference(cnf_transformation,[],[f46]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( tc(X0,lam(X1),arr(X2,X3))
| ~ tc(cons(X2,X0),X1,X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f66,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,[],[f49]) ).
fof(f74,plain,
! [X0,X1] : lam(X0) != var(X1),
inference(cnf_transformation,[],[f23]) ).
fof(f77,plain,
! [X2,X3,X0,X1] : app(X0,X1,X2) != lam(X3),
inference(cnf_transformation,[],[f21]) ).
fof(f82,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f29]) ).
fof(f85,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f30]) ).
fof(f93,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f59]) ).
fof(f100,plain,
! [X2,X0,X1] :
( just(X0) != just(X2)
| tc(cons(X0,X1),var(zero),X2) ),
inference(superposition,[],[f93,f82]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( just(X3) != index(X0,X1)
| tc(cons(X2,X0),var(suc(X1)),X3) ),
inference(superposition,[],[f93,f85]) ).
fof(f102,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[],[f100]) ).
fof(f103,plain,
! [X0] :
( ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b))
| ~ nf(lam(X0)) ),
inference(resolution,[],[f62,f50]) ).
fof(f107,plain,
! [X0] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b)
| ~ nf(lam(lam(X0))) ),
inference(resolution,[],[f103,f62]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X1,b))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,X1)
| ~ nf(lam(lam(app(X0,X2,X1)))) ),
inference(resolution,[],[f66,f107]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( just(X0) != just(X1)
| tc(cons(X3,cons(X0,X2)),var(suc(zero)),X1) ),
inference(superposition,[],[f101,f82]) ).
fof(f147,plain,
! [X2,X0,X1] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[],[f128]) ).
fof(f159,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,arr(X4,arr(X1,b)))
| ~ nf(lam(lam(app(app(X2,X3,X4),X0,X1))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,X1)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X4) ),
inference(resolution,[],[f124,f66]) ).
fof(f225,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ nf(lam(lam(app(app(var(suc(zero)),X0,a),X1,a))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[],[f159,f147]) ).
fof(f241,plain,
! [X0] :
( ~ nf(lam(lam(app(app(var(suc(zero)),X0,a),var(zero),a))))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[],[f225,f102]) ).
fof(f244,plain,
! [X0] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a)
| ~ nf(lam(app(app(var(suc(zero)),X0,a),var(zero),a))) ),
inference(resolution,[],[f241,f53]) ).
fof(f249,plain,
~ nf(lam(app(app(var(suc(zero)),var(zero),a),var(zero),a))),
inference(resolution,[],[f244,f102]) ).
fof(f254,plain,
~ nf(app(app(var(suc(zero)),var(zero),a),var(zero),a)),
inference(resolution,[],[f249,f53]) ).
fof(f256,plain,
( ~ nf(app(var(suc(zero)),var(zero),a))
| ~ nf(var(zero))
| app(var(suc(zero)),var(zero),a) = lam(proj1Lam(app(var(suc(zero)),var(zero),a))) ),
inference(resolution,[],[f254,f57]) ).
fof(f257,plain,
( ~ nf(app(var(suc(zero)),var(zero),a))
| app(var(suc(zero)),var(zero),a) = lam(proj1Lam(app(var(suc(zero)),var(zero),a))) ),
inference(forward_subsumption_resolution,[],[f256,f51]) ).
fof(f258,plain,
~ nf(app(var(suc(zero)),var(zero),a)),
inference(forward_subsumption_resolution,[],[f257,f77]) ).
fof(f262,plain,
( ~ nf(var(suc(zero)))
| ~ nf(var(zero))
| var(suc(zero)) = lam(proj1Lam(var(suc(zero)))) ),
inference(resolution,[],[f258,f57]) ).
fof(f263,plain,
( ~ nf(var(suc(zero)))
| var(suc(zero)) = lam(proj1Lam(var(suc(zero)))) ),
inference(forward_subsumption_resolution,[],[f262,f51]) ).
fof(f264,plain,
var(suc(zero)) = lam(proj1Lam(var(suc(zero)))),
inference(forward_subsumption_resolution,[],[f263,f51]) ).
fof(f265,plain,
$false,
inference(forward_subsumption_resolution,[],[f264,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX223+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n002.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Mon Sep 28 15:15:37 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running first-order theorem proving
% 0.12/0.23 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
% 2.81/1.13 % (437110)Detected formulas, will run a generic FOF schedule.
% 2.81/1.13 % (437248)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2106252201:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.81/1.13 % (437248)Instruction limit reached!
% 2.81/1.13 % (437248)------------------------------
% 2.81/1.13 % (437248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.13 % (437248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.13 % (437248)CaDiCaL version: 2.1.3
% 2.81/1.13 % (437248)Termination reason: Instruction limit
% 2.81/1.13 % (437248)Termination phase: Saturation
% 2.81/1.13 % (437248)Time elapsed: 0.037 s
% 2.81/1.13 % (437248)Peak memory usage: 89 MB
% 2.81/1.13 % (437248)Instructions burned: 109 (million)
% 2.81/1.13 % (437251)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=662775325:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.81/1.13 % (437247)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=623155050:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.81/1.13 % (437243)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=2627090320:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.81/1.13 % (437250)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3894040988:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.81/1.13 % (437245)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=12123178:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.81/1.13 % (437252)dis-21_1_sil=8000:lcm=predicate:random_seed=2093976100: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)
% 2.81/1.13 % (437250)Instruction limit reached!
% 2.81/1.13 % (437250)------------------------------
% 2.81/1.13 % (437250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.13 % (437250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.13 % (437250)CaDiCaL version: 2.1.3
% 2.81/1.13 % (437250)Termination reason: Instruction limit
% 2.81/1.13 % (437250)Termination phase: Saturation
% 2.81/1.13 % (437250)Time elapsed: 0.069 s
% 2.81/1.13 % (437250)Peak memory usage: 88 MB
% 2.81/1.13 % (437250)Instructions burned: 119 (million)
% 2.81/1.13 % (437251)Instruction limit reached!
% 2.81/1.13 % (437251)------------------------------
% 2.81/1.13 % (437251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.13 % (437251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.13 % (437251)CaDiCaL version: 2.1.3
% 2.81/1.13 % (437251)Termination reason: Instruction limit
% 2.81/1.13 % (437251)Termination phase: Saturation
% 2.81/1.13 % (437251)Time elapsed: 0.088 s
% 2.81/1.13 % (437251)Peak memory usage: 89 MB
% 2.81/1.13 % (437251)Instructions burned: 141 (million)
% 2.81/1.13 % (437252)Instruction limit reached!
% 2.81/1.13 % (437252)------------------------------
% 2.81/1.13 % (437252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.13 % (437252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.13 % (437252)CaDiCaL version: 2.1.3
% 2.81/1.13 % (437252)Termination reason: Instruction limit
% 2.81/1.13 % (437252)Termination phase: Saturation
% 2.81/1.13 % (437252)Time elapsed: 0.081 s
% 2.81/1.13 % (437252)Peak memory usage: 89 MB
% 2.81/1.13 % (437252)Instructions burned: 130 (million)
% 2.81/1.13 % (437293)lrs+10_1_sil=8000:sp=occurrence:random_seed=576763853:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.81/1.13 % (437293)First to succeed.
% 2.81/1.13 % (437293)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-437110"
% 2.81/1.13 % (437300)lrs+10_1_sil=32000:urr=on:br=off:random_seed=731014098:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.81/1.13 % (437301)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3753903953:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.81/1.13 % (437302)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=2019226389:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.61/1.23 % (437293)Refutation found. Thanks to Tanya!
% 3.61/1.23 % SZS status Theorem for theBenchmark
% 3.61/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.23 % (437293)------------------------------
% 3.61/1.23 % (437293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.23 % (437293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.23 % (437293)CaDiCaL version: 2.1.3
% 3.61/1.23 % (437293)Termination reason: Refutation
% 3.61/1.23 % (437293)Time elapsed: 0.009 s
% 3.61/1.23 % (437293)Peak memory usage: 88 MB
% 3.61/1.23 % (437293)Instructions burned: 22 (million)
% 3.61/1.23 % (437293)------------------------------
% 3.61/1.23 % (437293)------------------------------
% 3.61/1.23 % (437110)Success in time 0.437 s
% 3.61/1.23 % Vampire exiting
%------------------------------------------------------------------------------