%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC007+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:02:00 PM UTC 2026
% Result : Theorem 3.52s 1.37s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 127 ( 54 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 169 ( 73 ~; 57 |; 29 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 43 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X2
| X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X2
| X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X2
& X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X2
& X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0 ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f108,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
( nil = sK2
& sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f125,plain,
ssList(sK2),
inference(cnf_transformation,[],[f118]) ).
fof(f126,plain,
ssList(sK3),
inference(cnf_transformation,[],[f118]) ).
fof(f127,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK1
| app(X4,X6) != sK0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f128,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f118]) ).
fof(f129,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
nil = sK2,
inference(cnf_transformation,[],[f118]) ).
fof(f131,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f139,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f154,plain,
! [X6,X4,X5] :
( app(app(X4,X5),X6) != sK3
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssList(X4)
| app(X4,X6) != sK2 ),
inference(definition_unfolding,[],[f127,f129,f128]) ).
fof(f157,plain,
! [X0] :
( app(X0,sK2) = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f131,f130]) ).
fof(f162,plain,
! [X0] :
( app(sK2,X0) = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f139,f130]) ).
fof(f181,plain,
! [X0,X1] :
( app(X0,X1) != sK3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK2)
| sK2 != app(sK2,X1)
| ~ ssList(X0) ),
inference(superposition,[],[f154,f162]) ).
fof(f185,plain,
! [X0,X1] :
( app(X0,X1) != sK3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK2)
| sK2 != app(sK2,X1) ),
inference(duplicate_literal_removal,[],[f181]) ).
fof(f188,plain,
! [X0,X1] :
( sK2 != app(sK2,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != sK3 ),
inference(forward_subsumption_resolution,[],[f185,f125]) ).
fof(f191,plain,
! [X0] :
( sK2 != sK2
| ~ ssList(X0)
| ~ ssList(sK2)
| sK3 != app(X0,sK2)
| ~ ssList(sK2) ),
inference(superposition,[],[f188,f157]) ).
fof(f192,plain,
! [X0] :
( sK2 != sK2
| ~ ssList(X0)
| ~ ssList(sK2)
| sK3 != app(X0,sK2) ),
inference(duplicate_literal_removal,[],[f191]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK2)
| sK3 != app(X0,sK2) ),
inference(trivial_inequality_removal,[],[f192]) ).
fof(f195,plain,
! [X0] :
( sK3 != app(X0,sK2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f193,f125]) ).
fof(f196,plain,
! [X0] :
( sK3 != X0
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(superposition,[],[f195,f157]) ).
fof(f200,plain,
! [X0] :
( sK3 != X0
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f203,plain,
~ ssList(sK3),
inference(equality_resolution,[],[f200]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC007+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 07:25:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 3.52/1.37 % (1606795)Detected formulas, will run a generic FOF schedule.
% 3.52/1.37 % (1606806)dis-21_1_sil=8000:lcm=predicate:random_seed=553372302: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)
% 3.52/1.37 % (1606806)Instruction limit reached!
% 3.52/1.37 % (1606806)------------------------------
% 3.52/1.37 % (1606806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (1606806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (1606806)CaDiCaL version: 2.1.3
% 3.52/1.37 % (1606806)Termination reason: Instruction limit
% 3.52/1.37 % (1606806)Termination phase: Saturation
% 3.52/1.37 % (1606806)Time elapsed: 0.040 s
% 3.52/1.37 % (1606806)Peak memory usage: 90 MB
% 3.52/1.37 % (1606806)Instructions burned: 132 (million)
% 3.52/1.37 % (1606802)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=1746933815:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.52/1.37 % (1606800)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=3739108114:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.52/1.37 % (1606804)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1569598214:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.52/1.37 % (1606803)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=358323523:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.52/1.37 % (1606801)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=729871349:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.52/1.37 % (1606805)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1263494334:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.52/1.37 % (1606804)First to succeed.
% 3.52/1.37 % (1606804)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1606795"
% 3.52/1.37 % (1606805)Also succeeded, but the first one will report.
% 3.52/1.37 % (1606803)Also succeeded, but the first one will report.
% 3.52/1.37 % (1606814)lrs+10_1_sil=8000:sp=occurrence:random_seed=355698840:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.52/1.37 % (1606814)Also succeeded, but the first one will report.
% 3.52/1.37 % (1606804)Refutation found. Thanks to Tanya!
% 3.52/1.37 % SZS status Theorem for theBenchmark
% 3.52/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.37 % (1606804)------------------------------
% 3.52/1.37 % (1606804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (1606804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (1606804)CaDiCaL version: 2.1.3
% 3.52/1.37 % (1606804)Termination reason: Refutation
% 3.52/1.37 % (1606804)Time elapsed: 0.004 s
% 3.52/1.37 % (1606804)Peak memory usage: 88 MB
% 3.52/1.37 % (1606804)Instructions burned: 4 (million)
% 3.52/1.37 % (1606804)------------------------------
% 3.52/1.37 % (1606804)------------------------------
% 3.52/1.37 % (1606795)Success in time 0.437 s
% 3.52/1.37 % Vampire exiting
%------------------------------------------------------------------------------