%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC404+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 : n008.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 01:03:50 PM UTC 2026
% Result : Theorem 2.69s 1.17s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 243 ( 48 equ)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 328 ( 120 ~; 112 |; 75 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 99 ( 69 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ! [X14] :
( ssItem(X14)
=> ( ~ memberP(X0,X14)
| memberP(X1,X14) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
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] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ! [X14] :
( ssItem(X14)
=> ( ~ memberP(X0,X14)
| memberP(X1,X14) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ? [X14] :
( memberP(X0,X14)
& ~ memberP(X1,X14)
& ssItem(X14) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ? [X14] :
( memberP(X0,X14)
& ~ memberP(X1,X14)
& ssItem(X14) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f148,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(app(sK4,sK2),sK5)
& strictorderedP(sK2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != sK2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != sK5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != sK2
| ~ lt(X12,X10) ) ) ) )
& ssList(sK5)
& ssList(sK4)
& memberP(sK0,sK6)
& ~ memberP(sK1,sK6)
& ssItem(sK6)
& ( nil = sK3
| nil != sK2 )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X14,sK6)],[f99]) ).
fof(f155,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f155]) ).
fof(f170,plain,
ssList(sK2),
inference(cnf_transformation,[],[f148]) ).
fof(f173,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f148]) ).
fof(f174,plain,
~ memberP(sK1,sK6),
inference(cnf_transformation,[],[f148]) ).
fof(f175,plain,
memberP(sK0,sK6),
inference(cnf_transformation,[],[f148]) ).
fof(f176,plain,
ssList(sK4),
inference(cnf_transformation,[],[f148]) ).
fof(f177,plain,
ssList(sK5),
inference(cnf_transformation,[],[f148]) ).
fof(f181,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f148]) ).
fof(f182,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f148]) ).
fof(f183,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f148]) ).
fof(f205,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f212,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f213,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f249,plain,
memberP(sK2,sK6),
inference(definition_unfolding,[],[f175,f182]) ).
fof(f250,plain,
~ memberP(sK3,sK6),
inference(definition_unfolding,[],[f174,f183]) ).
fof(f369,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(app(sK4,sK2),X0)
| ~ ssList(sK5)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0) ),
inference(superposition,[],[f213,f181]) ).
fof(f374,plain,
! [X0] :
( ~ memberP(app(sK4,sK2),X0)
| memberP(sK3,X0)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f369,f177]) ).
fof(f389,plain,
! [X0] :
( memberP(sK3,X0)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssList(sK4)
| ~ ssItem(X0) ),
inference(resolution,[],[f374,f212]) ).
fof(f390,plain,
! [X0] :
( memberP(sK3,X0)
| ~ ssList(app(sK4,sK2))
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssList(sK4) ),
inference(duplicate_literal_removal,[],[f389]) ).
fof(f392,plain,
! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK2)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f390,f205]) ).
fof(f394,plain,
! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssList(sK4) ),
inference(forward_subsumption_resolution,[],[f392,f170]) ).
fof(f396,plain,
! [X0] :
( memberP(sK3,X0)
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f394,f176]) ).
fof(f405,plain,
( ~ ssItem(sK6)
| ~ memberP(sK2,sK6) ),
inference(resolution,[],[f396,f250]) ).
fof(f406,plain,
~ memberP(sK2,sK6),
inference(forward_subsumption_resolution,[],[f405,f173]) ).
fof(f407,plain,
$false,
inference(forward_subsumption_resolution,[],[f406,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC404+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 09:31:40 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 2.69/1.17 % (2123098)Detected formulas, will run a generic FOF schedule.
% 2.69/1.17 % (2123107)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1190890038:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.17 % (2123107)First to succeed.
% 2.69/1.17 % (2123107)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2123098"
% 2.69/1.17 % (2123103)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=2451567592:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.17 % (2123104)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=3052994:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.17 % (2123109)dis-21_1_sil=8000:lcm=predicate:random_seed=2223147079: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)
% 2.69/1.17 % (2123106)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2294735773:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.17 % (2123105)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=1118299679:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.17 % (2123108)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1731587922:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.17 % (2123106)Also succeeded, but the first one will report.
% 2.69/1.17 % (2123109)Instruction limit reached!
% 2.69/1.17 % (2123109)------------------------------
% 2.69/1.17 % (2123109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.17 % (2123109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.17 % (2123109)CaDiCaL version: 2.1.3
% 2.69/1.17 % (2123109)Termination reason: Instruction limit
% 2.69/1.17 % (2123109)Termination phase: Saturation
% 2.69/1.17 % (2123109)Time elapsed: 0.070 s
% 2.69/1.17 % (2123109)Peak memory usage: 90 MB
% 2.69/1.17 % (2123109)Instructions burned: 130 (million)
% 2.69/1.17 % (2123108)Instruction limit reached!
% 2.69/1.17 % (2123108)------------------------------
% 2.69/1.17 % (2123108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.17 % (2123108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.17 % (2123108)CaDiCaL version: 2.1.3
% 2.69/1.17 % (2123108)Termination reason: Instruction limit
% 2.69/1.17 % (2123108)Termination phase: Saturation
% 2.69/1.17 % (2123108)Time elapsed: 0.094 s
% 2.69/1.17 % (2123108)Peak memory usage: 91 MB
% 2.69/1.17 % (2123108)Instructions burned: 140 (million)
% 2.69/1.17 % (2123107)Refutation found. Thanks to Tanya!
% 2.69/1.17 % SZS status Theorem for theBenchmark
% 2.69/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.17 % (2123107)------------------------------
% 2.69/1.17 % (2123107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.17 % (2123107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.17 % (2123107)CaDiCaL version: 2.1.3
% 2.69/1.17 % (2123107)Termination reason: Refutation
% 2.69/1.17 % (2123107)Time elapsed: 0.005 s
% 2.69/1.17 % (2123107)Peak memory usage: 88 MB
% 2.69/1.17 % (2123107)Instructions burned: 12 (million)
% 2.69/1.17 % (2123107)------------------------------
% 2.69/1.17 % (2123107)------------------------------
% 2.69/1.17 % (2123098)Success in time 0.287 s
% 2.69/1.17 % Vampire exiting
%------------------------------------------------------------------------------