%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW508_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 01:30:43 PM UTC 2026
% Result : Theorem 1.00s 0.95s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 32 ~; 28 |; 10 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-6 aty)
% Number of functors : 41 ( 41 usr; 13 con; 0-10 aty)
% Number of variables : 50 ( 40 !; 10 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
com: $tType ).
tff(type_def_7,type,
loc: $tType ).
tff(type_def_8,type,
pname: $tType ).
tff(type_def_9,type,
state: $tType ).
tff(type_def_10,type,
vname: $tType ).
tff(type_def_11,type,
bool: $tType ).
tff(type_def_12,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_13,type,
nat: $tType ).
tff(type_def_14,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
skip: com ).
tff(func_def_5,type,
semi: ( com * com ) > com ).
tff(func_def_6,type,
com_case:
!>[X0: $tType] : ( ( X0 * fun(vname,fun(fun(state,nat),X0)) * fun(loc,fun(fun(state,nat),fun(com,X0))) * fun(com,fun(com,X0)) * fun(fun(state,bool),fun(com,fun(com,X0))) * fun(fun(state,bool),fun(com,X0)) * fun(pname,X0) * fun(vname,fun(pname,fun(fun(state,nat),X0))) * com ) > X0 ) ).
tff(func_def_7,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_8,type,
hoare_1841697145triple:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(X0,fun(state,bool)) ) > hoare_28830079triple(X0) ) ).
tff(func_def_9,type,
hoare_376461865e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).
tff(func_def_10,type,
hoare_678420151le_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(fun(X0,fun(state,bool)),fun(com,fun(fun(X0,fun(state,bool)),X1))) * hoare_28830079triple(X0) ) > X1 ) ).
tff(func_def_11,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_12,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_13,type,
insert:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > fun(X0,bool) ) ).
tff(func_def_14,type,
the_elem:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fNot: fun(bool,bool) ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_20,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_22,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_24,type,
g: fun(hoare_28830079triple(a),bool) ).
tff(func_def_25,type,
p1: fun(a,fun(state,bool)) ).
tff(func_def_26,type,
q1: fun(a,fun(state,bool)) ).
tff(func_def_27,type,
c: com ).
tff(func_def_28,type,
sK0: ( state * state ) > a ).
tff(func_def_29,type,
sK1: a ).
tff(func_def_30,type,
sK2: state ).
tff(func_def_31,type,
sK3: ( fun(a,fun(state,bool)) * fun(a,fun(state,bool)) ) > state ).
tff(func_def_32,type,
sK4:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_33,type,
sK5:
!>[X0: $tType] : ( hoare_28830079triple(X0) > com ) ).
tff(func_def_34,type,
sK6:
!>[X0: $tType] : ( hoare_28830079triple(X0) > fun(X0,fun(state,bool)) ) ).
tff(func_def_35,type,
sK7:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > X0 ) ).
tff(func_def_36,type,
sK8:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_37,type,
sK9:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * com * fun(hoare_28830079triple(X0),bool) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) * fun(X0,fun(state,bool)) ) > state ) ).
tff(func_def_38,type,
sK10:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
finite_finite:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
finite_finite1:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_5,type,
finite_fold1Set:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(X0,bool) * X0 ) > $o ) ).
tff(pred_def_6,type,
finite_fold_graph:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * X1 * fun(X0,bool) * X1 ) > $o ) ).
tff(pred_def_7,type,
finite_folding_one:
!>[X0: $tType] : ( ( fun(X0,fun(X0,X0)) * fun(fun(X0,bool),X0) ) > $o ) ).
tff(pred_def_8,type,
hoare_992312373derivs:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_9,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(pred_def_11,type,
p: ( a * state ) > $o ).
tff(pred_def_12,type,
q: ( a * state ) > $o ).
tff(f128,axiom,
hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,p1,c,q1),bot_bot(fun(hoare_28830079triple(a),bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f129,axiom,
! [X0: a,X1: state] :
( p(X0,X1)
=> ! [X2: state] :
( ! [X3: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),p1,X3),X1))
=> pp(aa(state,bool,aa(a,fun(state,bool),q1,X3),X2)) )
=> q(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f130,conjecture,
! [X0: a,X1: state] :
( ~ p(X0,X1)
| ? [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
& ! [X4: state] :
( ? [X5: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
& ~ pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
| q(X0,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f131,negated_conjecture,
~ ! [X0: a,X1: state] :
( ~ p(X0,X1)
| ? [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
& ! [X4: state] :
( ? [X5: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
& ~ pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
| q(X0,X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f130]) ).
tff(f133,plain,
! [X0: a,X1: state] :
( ! [X2: state] :
( q(X0,X2)
| ? [X3: a] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),q1,X3),X2))
& pp(aa(state,bool,aa(a,fun(state,bool),p1,X3),X1)) ) )
| ~ p(X0,X1) ),
inference(ennf_transformation,[],[f129]) ).
tff(f134,plain,
? [X0: a,X1: state] :
( p(X0,X1)
& ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
| ? [X4: state] :
( ! [X5: a] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),X1))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),X4)) )
& ~ q(X0,X4) ) ) ),
inference(ennf_transformation,[],[f131]) ).
tff(f143,plain,
! [X0: a,X1: state] :
( ! [X2: state] :
( q(X0,X2)
| ( ~ pp(aa(state,bool,aa(a,fun(state,bool),q1,sK0(X1,X2)),X2))
& pp(aa(state,bool,aa(a,fun(state,bool),p1,sK0(X1,X2)),X1)) ) )
| ~ p(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X1,X2))],[f133]) ).
tff(f144,plain,
( p(sK1,sK2)
& ! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
| ( ! [X5: a] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK2))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK3(X2,X3))) )
& ~ q(sK1,sK3(X2,X3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X4,sK3(X2,X3))],[f134]) ).
tff(f154,plain,
hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,p1,c,q1),bot_bot(fun(hoare_28830079triple(a),bool)))),
inference(cnf_transformation,[],[f128]) ).
tff(f155,plain,
! [X2: state,X0: a,X1: state] :
( pp(aa(state,bool,aa(a,fun(state,bool),p1,sK0(X1,X2)),X1))
| q(X0,X2)
| ~ p(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tff(f156,plain,
! [X2: state,X0: a,X1: state] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),q1,sK0(X1,X2)),X2))
| q(X0,X2)
| ~ p(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tff(f157,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool))] :
( ~ hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ q(sK1,sK3(X2,X3)) ),
inference(cnf_transformation,[],[f144]) ).
tff(f158,plain,
! [X2: fun(a,fun(state,bool)),X3: fun(a,fun(state,bool)),X5: a] :
( ~ hoare_992312373derivs(a,g,insert(hoare_28830079triple(a),hoare_1841697145triple(a,X2,c,X3),bot_bot(fun(hoare_28830079triple(a),bool))))
| ~ pp(aa(state,bool,aa(a,fun(state,bool),X2,X5),sK2))
| pp(aa(state,bool,aa(a,fun(state,bool),X3,X5),sK3(X2,X3))) ),
inference(cnf_transformation,[],[f144]) ).
tff(f159,plain,
p(sK1,sK2),
inference(cnf_transformation,[],[f144]) ).
tff(f229,plain,
! [X0: a] :
( pp(aa(state,bool,aa(a,fun(state,bool),q1,X0),sK3(p1,q1)))
| ~ pp(aa(state,bool,aa(a,fun(state,bool),p1,X0),sK2)) ),
inference(resolution,[],[f154,f158]) ).
tff(f230,plain,
~ q(sK1,sK3(p1,q1)),
inference(resolution,[],[f154,f157]) ).
tff(f264,plain,
! [X0: a,X1: state] :
( ~ pp(aa(state,bool,aa(a,fun(state,bool),p1,sK0(X1,sK3(p1,q1))),sK2))
| ~ p(X0,X1)
| q(X0,sK3(p1,q1)) ),
inference(resolution,[],[f156,f229]) ).
tff(f265,plain,
! [X0: a,X1: a] :
( q(X1,sK3(p1,q1))
| q(X0,sK3(p1,q1))
| ~ p(X0,sK2)
| ~ p(X1,sK2) ),
inference(resolution,[],[f264,f155]) ).
tff(f266,plain,
! [X0: a] :
( q(X0,sK3(p1,q1))
| ~ p(X0,sK2)
| ~ p(sK1,sK2) ),
inference(resolution,[],[f265,f230]) ).
tff(f267,plain,
! [X0: a] :
( q(X0,sK3(p1,q1))
| ~ p(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f266,f159]) ).
tff(f269,plain,
~ p(sK1,sK2),
inference(resolution,[],[f267,f230]) ).
tff(f270,plain,
$false,
inference(forward_subsumption_resolution,[],[f269,f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW508_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 14:14:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 1.00/0.95 % (1206114)Detected formulas, will run a generic FOF schedule.
% 1.00/0.95 % (1206123)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1424376511:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.00/0.95 % (1206123)First to succeed.
% 1.00/0.95 % (1206123)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1206114"
% 1.00/0.95 % (1206124)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1428691102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.00/0.95 % (1206120)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=3335977380:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.00/0.95 % (1206122)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3439995617:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.00/0.95 % (1206121)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=2489111681:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.00/0.95 % (1206119)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=4087377414:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.00/0.95 % (1206125)dis-21_1_sil=8000:lcm=predicate:random_seed=2195419744: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)
% 1.00/0.95 % (1206122)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.00/0.95 % (1206122)Also succeeded, but the first one will report.
% 1.00/0.95 % (1206121)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.00/0.95 % (1206125)Instruction limit reached!
% 1.00/0.95 % (1206125)------------------------------
% 1.00/0.95 % (1206125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.00/0.95 % (1206125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.95 % (1206125)CaDiCaL version: 2.1.3
% 1.00/0.95 % (1206125)Termination reason: Instruction limit
% 1.00/0.95 % (1206125)Termination phase: Saturation
% 1.00/0.95 % (1206125)Time elapsed: 0.052 s
% 1.00/0.95 % (1206125)Peak memory usage: 88 MB
% 1.00/0.95 % (1206125)Instructions burned: 129 (million)
% 1.00/0.95 % (1206124)Instruction limit reached!
% 1.00/0.95 % (1206124)------------------------------
% 1.00/0.95 % (1206124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.00/0.95 % (1206124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.95 % (1206124)CaDiCaL version: 2.1.3
% 1.00/0.95 % (1206124)Termination reason: Instruction limit
% 1.00/0.95 % (1206124)Termination phase: Saturation
% 1.00/0.95 % (1206124)Time elapsed: 0.067 s
% 1.00/0.95 % (1206124)Peak memory usage: 89 MB
% 1.00/0.95 % (1206124)Instructions burned: 140 (million)
% 1.00/0.95 % (1206123)Refutation found. Thanks to Tanya!
% 1.00/0.95 % SZS status Theorem for theBenchmark
% 1.00/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.48/1.14 % (1206123)------------------------------
% 2.48/1.14 % (1206123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.48/1.14 % (1206123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.48/1.14 % (1206123)CaDiCaL version: 2.1.3
% 2.48/1.14 % (1206123)Termination reason: Refutation
% 2.48/1.14 % (1206123)Time elapsed: 0.005 s
% 2.48/1.14 % (1206123)Peak memory usage: 89 MB
% 2.48/1.14 % (1206123)Instructions burned: 11 (million)
% 2.48/1.14 % (1206123)------------------------------
% 2.48/1.14 % (1206123)------------------------------
% 2.48/1.14 % (1206114)Success in time 0.279 s
% 2.48/1.14 % Vampire exiting
%------------------------------------------------------------------------------