%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:02:06 PM UTC 2026
% Result : Theorem 0.16s 1.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 9 unt; 0 def)
% Number of atoms : 165 ( 86 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 194 ( 69 ~; 63 |; 49 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( nil != X0
| nil = X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( nil = X0
& nil != X1 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f107,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f127,plain,
( sK1 = sK3
& sK0 = sK2
& ( ( sK2 = cons(sK4,nil)
& memberP(sK3,sK4)
& ! [X5] :
( ~ ssItem(X5)
| sK4 = X5
| ~ memberP(sK3,X5)
| ~ leq(sK4,X5) )
& ssItem(sK4) )
| ( nil = sK3
& nil = sK2 ) )
& ( ( nil = sK1
& nil != sK0 )
| ( nil = sK0
& nil != sK1 ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f141,plain,
ssList(sK2),
inference(cnf_transformation,[],[f127]) ).
fof(f143,plain,
( nil != sK0
| nil != sK1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f146,plain,
( nil = sK1
| nil = sK0 ),
inference(cnf_transformation,[],[f127]) ).
fof(f147,plain,
( nil = sK2
| ssItem(sK4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f148,plain,
( nil = sK3
| ssItem(sK4) ),
inference(cnf_transformation,[],[f127]) ).
fof(f151,plain,
( memberP(sK3,sK4)
| nil = sK2 ),
inference(cnf_transformation,[],[f127]) ).
fof(f154,plain,
( sK2 = cons(sK4,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f155,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f127]) ).
fof(f156,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f127]) ).
fof(f160,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f169,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f194,plain,
( nil = sK3
| nil = sK2 ),
inference(definition_unfolding,[],[f146,f156,f155]) ).
fof(f197,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f143,f155,f156]) ).
fof(f207,plain,
( sK2 = sK3
| ssItem(sK4)
| ssItem(sK4) ),
inference(superposition,[],[f147,f148]) ).
fof(f208,plain,
( sK2 = sK3
| ssItem(sK4) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f217,plain,
( sK2 != sK3
| sK2 != sK2
| ssItem(sK4) ),
inference(superposition,[],[f197,f147]) ).
fof(f218,plain,
( sK2 != sK3
| ssItem(sK4) ),
inference(trivial_inequality_removal,[],[f217]) ).
fof(f221,plain,
ssItem(sK4),
inference(forward_subsumption_resolution,[],[f218,f208]) ).
fof(f233,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0)
| nil = sK2 ),
inference(superposition,[],[f169,f194]) ).
fof(f237,plain,
( ~ ssItem(sK4)
| nil = sK2
| nil = sK2 ),
inference(resolution,[],[f233,f151]) ).
fof(f239,plain,
( ~ ssItem(sK4)
| nil = sK2 ),
inference(duplicate_literal_removal,[],[f237]) ).
fof(f240,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f239,f147]) ).
fof(f249,plain,
( sK2 = cons(sK4,sK2)
| sK2 = sK3 ),
inference(superposition,[],[f154,f240]) ).
fof(f252,plain,
( sK2 != sK3
| sK2 != sK2 ),
inference(superposition,[],[f197,f240]) ).
fof(f253,plain,
sK2 != sK3,
inference(trivial_inequality_removal,[],[f252]) ).
fof(f257,plain,
sK2 = cons(sK4,sK2),
inference(forward_subsumption_resolution,[],[f249,f253]) ).
fof(f273,plain,
! [X0,X1] :
( cons(X1,X0) != sK2
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f160,f240]) ).
fof(f277,plain,
( sK2 != sK2
| ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f273,f257]) ).
fof(f278,plain,
( ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f277]) ).
fof(f282,plain,
~ ssList(sK2),
inference(forward_subsumption_resolution,[],[f278,f221]) ).
fof(f284,plain,
$false,
inference(forward_subsumption_resolution,[],[f282,f141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n010.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 07:31:03 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 0.16/1.50 % (1740579)Detected formulas, will run a generic FOF schedule.
% 0.16/1.50 % (1740585)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=1110301204:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.50 % (1740587)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=89550327:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.50 % (1740586)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=2422766432:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.50 % (1740588)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3236659052:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.50 % (1740584)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=4280527404:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.50 % (1740589)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3756093244:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.50 % (1740588)First to succeed.
% 0.16/1.50 % (1740590)dis-21_1_sil=8000:lcm=predicate:random_seed=542803836: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)
% 0.16/1.50 % (1740587)Also succeeded, but the first one will report.
% 0.16/1.50 % (1740588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1740579"
% 0.16/1.50 % (1740589)Also succeeded, but the first one will report.
% 0.16/1.50 % (1740590)Instruction limit reached!
% 0.16/1.50 % (1740590)------------------------------
% 0.16/1.50 % (1740590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1740590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1740590)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1740590)Termination reason: Instruction limit
% 0.16/1.50 % (1740590)Termination phase: Saturation
% 0.16/1.50 % (1740590)Time elapsed: 0.070 s
% 0.16/1.50 % (1740590)Peak memory usage: 91 MB
% 0.16/1.50 % (1740590)Instructions burned: 129 (million)
% 0.16/1.50 % (1740598)lrs+10_1_sil=8000:sp=occurrence:random_seed=1407099434:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.16/1.50 % (1740598)Also succeeded, but the first one will report.
% 0.16/1.50 % (1740588)Refutation found. Thanks to Tanya!
% 0.16/1.50 % SZS status Theorem for theBenchmark
% 0.16/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (1740588)------------------------------
% 0.16/1.50 % (1740588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1740588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1740588)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1740588)Termination reason: Refutation
% 0.16/1.50 % (1740588)Time elapsed: 0.005 s
% 0.16/1.50 % (1740588)Peak memory usage: 88 MB
% 0.16/1.50 % (1740588)Instructions burned: 5 (million)
% 0.16/1.50 % (1740588)------------------------------
% 0.16/1.50 % (1740588)------------------------------
% 0.16/1.50 % (1740579)Success in time 0.421 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------