%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW513_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 : 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 01:30:43 PM UTC 2026
% Result : Theorem 2.59s 1.06s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-6 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-5 aty)
% Number of variables : 29 ( 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
state: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_9,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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_3,type,
uminus_uminus:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_4,type,
ord_Least:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_5,type,
ord_less_eq:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_6,type,
powp:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).
tff(func_def_7,type,
ord_atLeast:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_8,type,
ord_atMost:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_9,type,
ord_greaterThan:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_10,type,
ord_lessThan:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_11,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_12,type,
pow:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(X0,bool),bool) ) ).
tff(func_def_13,type,
image:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > fun(fun(X0,bool),fun(X1,bool)) ) ).
tff(func_def_14,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_15,type,
fFalse: bool ).
tff(func_def_16,type,
fNot: fun(bool,bool) ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_19,type,
g: fun(hoare_28830079triple(a),bool) ).
tff(func_def_20,type,
ga: fun(hoare_28830079triple(a),bool) ).
tff(func_def_21,type,
ts: fun(hoare_28830079triple(a),bool) ).
tff(func_def_22,type,
tsa: fun(hoare_28830079triple(a),bool) ).
tff(func_def_23,type,
sK0:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(pred_def_1,type,
enum:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
wellorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
enum_enum_all:
!>[X0: $tType] : ( fun(X0,bool) > $o ) ).
tff(pred_def_9,type,
hoare_992312373derivs:
!>[X0: $tType] : ( ( fun(hoare_28830079triple(X0),bool) * fun(hoare_28830079triple(X0),bool) ) > $o ) ).
tff(pred_def_10,type,
hoare_1442473487ek_and:
!>[X0: $tType] : ( ( fun(X0,fun(state,bool)) * fun(state,bool) * X0 * state ) > $o ) ).
tff(pred_def_11,type,
order_mono:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > $o ) ).
tff(pred_def_12,type,
order_strict_mono:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > $o ) ).
tff(pred_def_13,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f1,axiom,
! [X1: $tType,X3: fun(hoare_28830079triple(X1),bool),X4: fun(hoare_28830079triple(X1),bool)] :
( pp(aa(fun(hoare_28830079triple(X1),bool),bool,aa(fun(hoare_28830079triple(X1),bool),fun(fun(hoare_28830079triple(X1),bool),bool),ord_less_eq(fun(hoare_28830079triple(X1),bool)),X4),X3))
=> hoare_992312373derivs(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_asm) ).
tff(f3,axiom,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: fun(hoare_28830079triple(X0),bool),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X3,X2)
=> ( hoare_992312373derivs(X0,X1,X3)
=> hoare_992312373derivs(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut) ).
tff(f118,axiom,
pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(fun(hoare_28830079triple(a),bool),fun(fun(hoare_28830079triple(a),bool),bool),ord_less_eq(fun(hoare_28830079triple(a),bool)),tsa),ts)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f120,axiom,
hoare_992312373derivs(a,ga,ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
tff(f121,conjecture,
hoare_992312373derivs(a,ga,tsa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f122,negated_conjecture,
~ hoare_992312373derivs(a,ga,tsa),
inference(negated_conjecture,[status(cth)],[f121]) ).
tff(f123,plain,
~ hoare_992312373derivs(a,ga,tsa),
inference(flattening,[],[f122]) ).
tff(f124,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: fun(hoare_28830079triple(X0),bool)] :
( pp(aa(fun(hoare_28830079triple(X0),bool),bool,aa(fun(hoare_28830079triple(X0),bool),fun(fun(hoare_28830079triple(X0),bool),bool),ord_less_eq(fun(hoare_28830079triple(X0),bool)),X2),X1))
=> hoare_992312373derivs(X0,X1,X2) ),
inference(rectify,[],[f1]) ).
tff(f125,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: fun(hoare_28830079triple(X0),bool),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X1,X2)
| ~ hoare_992312373derivs(X0,X1,X3)
| ~ hoare_992312373derivs(X0,X3,X2) ),
inference(ennf_transformation,[],[f3]) ).
tff(f126,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: fun(hoare_28830079triple(X0),bool),X3: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X1,X2)
| ~ hoare_992312373derivs(X0,X1,X3)
| ~ hoare_992312373derivs(X0,X3,X2) ),
inference(flattening,[],[f125]) ).
tff(f136,plain,
! [X0: $tType,X1: fun(hoare_28830079triple(X0),bool),X2: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X1,X2)
| ~ pp(aa(fun(hoare_28830079triple(X0),bool),bool,aa(fun(hoare_28830079triple(X0),bool),fun(fun(hoare_28830079triple(X0),bool),bool),ord_less_eq(fun(hoare_28830079triple(X0),bool)),X2),X1)) ),
inference(ennf_transformation,[],[f124]) ).
tff(f139,plain,
pp(aa(fun(hoare_28830079triple(a),bool),bool,aa(fun(hoare_28830079triple(a),bool),fun(fun(hoare_28830079triple(a),bool),bool),ord_less_eq(fun(hoare_28830079triple(a),bool)),tsa),ts)),
inference(cnf_transformation,[],[f118]) ).
tff(f141,plain,
hoare_992312373derivs(a,ga,ts),
inference(cnf_transformation,[],[f120]) ).
tff(f142,plain,
~ hoare_992312373derivs(a,ga,tsa),
inference(cnf_transformation,[],[f123]) ).
tff(f143,plain,
! [X0: $tType,X2: fun(hoare_28830079triple(X0),bool),X3: fun(hoare_28830079triple(X0),bool),X1: fun(hoare_28830079triple(X0),bool)] :
( hoare_992312373derivs(X0,X1,X2)
| ~ hoare_992312373derivs(X0,X1,X3)
| ~ hoare_992312373derivs(X0,X3,X2) ),
inference(cnf_transformation,[],[f126]) ).
tff(f151,plain,
! [X0: $tType,X2: fun(hoare_28830079triple(X0),bool),X1: fun(hoare_28830079triple(X0),bool)] :
( ~ pp(aa(fun(hoare_28830079triple(X0),bool),bool,aa(fun(hoare_28830079triple(X0),bool),fun(fun(hoare_28830079triple(X0),bool),bool),ord_less_eq(fun(hoare_28830079triple(X0),bool)),X2),X1))
| hoare_992312373derivs(X0,X1,X2) ),
inference(cnf_transformation,[],[f136]) ).
tff(f152,plain,
! [X0: fun(hoare_28830079triple(a),bool)] :
( ~ hoare_992312373derivs(a,ga,X0)
| ~ hoare_992312373derivs(a,X0,tsa) ),
inference(resolution,[],[f143,f142]) ).
tff(f153,plain,
~ hoare_992312373derivs(a,ts,tsa),
inference(resolution,[],[f152,f141]) ).
tff(f169,plain,
hoare_992312373derivs(a,ts,tsa),
inference(resolution,[],[f151,f139]) ).
tff(f172,plain,
$false,
inference(forward_subsumption_resolution,[],[f169,f153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW513_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:18:22 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.59/1.06 % (378033)Detected formulas, will run a generic FOF schedule.
% 2.59/1.06 % (378042)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1385685352:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.06 % (378042)First to succeed.
% 2.59/1.06 % (378042)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-378033"
% 2.59/1.06 % (378038)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=3218677215:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.06 % (378039)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=2345980372:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.06 % (378040)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=1714526463:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.06 % (378041)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4094622411:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.06 % (378041)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.59/1.06 % (378041)Also succeeded, but the first one will report.
% 2.59/1.06 % (378040)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.59/1.06 % (378044)dis-21_1_sil=8000:lcm=predicate:random_seed=2743413884: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)
% 2.59/1.06 % (378043)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=455240650:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.06 % (378043)Also succeeded, but the first one will report.
% 2.59/1.06 % (378044)Instruction limit reached!
% 2.59/1.06 % (378044)------------------------------
% 2.59/1.06 % (378044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.06 % (378044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.06 % (378044)CaDiCaL version: 2.1.3
% 2.59/1.06 % (378044)Termination reason: Instruction limit
% 2.59/1.06 % (378044)Termination phase: Saturation
% 2.59/1.06 % (378044)Time elapsed: 0.051 s
% 2.59/1.06 % (378044)Peak memory usage: 88 MB
% 2.59/1.06 % (378044)Instructions burned: 130 (million)
% 2.59/1.06 % (378042)Refutation found. Thanks to Tanya!
% 2.59/1.06 % SZS status Theorem for theBenchmark
% 2.59/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.06 % (378042)------------------------------
% 2.59/1.06 % (378042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.06 % (378042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.06 % (378042)CaDiCaL version: 2.1.3
% 2.59/1.06 % (378042)Termination reason: Refutation
% 2.59/1.06 % (378042)Time elapsed: 0.002 s
% 2.59/1.06 % (378042)Peak memory usage: 88 MB
% 2.59/1.06 % (378042)Instructions burned: 3 (million)
% 2.59/1.06 % (378042)------------------------------
% 2.59/1.06 % (378042)------------------------------
% 2.59/1.06 % (378033)Success in time 0.298 s
% 2.59/1.06 % Vampire exiting
%------------------------------------------------------------------------------