%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW469_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 : n006.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 01:30:24 PM UTC 2026
% Result : Theorem 0.19s 1.14s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 3 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 2 prp; 0-5 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-4 aty)
% Number of variables : 18 ( 7 !; 11 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
com: $tType ).
tff(type_def_6,type,
state: $tType ).
tff(type_def_7,type,
node: ( $tType * $tType ) > $tType ).
tff(type_def_8,type,
bool: $tType ).
tff(type_def_9,type,
hoare_28830079triple: $tType > $tType ).
tff(type_def_10,type,
int: $tType ).
tff(type_def_11,type,
nat: $tType ).
tff(type_def_12,type,
char: $tType ).
tff(type_def_13,type,
literal: $tType ).
tff(type_def_14,type,
nibble: $tType ).
tff(type_def_15,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_16,type,
sum_sum: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_2,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bool_size: bool > nat ).
tff(func_def_5,type,
equal_equal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_6,type,
hoare_689268419triple:
!>[X0: $tType] : fun(fun(node(sum_sum(com,fun(X0,fun(state,bool))),sum_sum(state,X0)),bool),hoare_28830079triple(X0)) ).
tff(func_def_7,type,
hoare_334633230triple:
!>[X0: $tType] : fun(hoare_28830079triple(X0),fun(node(sum_sum(com,fun(X0,fun(state,bool))),sum_sum(state,X0)),bool)) ).
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,
hoare_711253694ep_set:
!>[X0: $tType] : fun(fun(node(sum_sum(com,fun(X0,fun(state,bool))),sum_sum(state,X0)),bool),bool) ).
tff(func_def_12,type,
hoare_47506394e_size:
!>[X0: $tType] : ( ( fun(X0,nat) * hoare_28830079triple(X0) ) > nat ) ).
tff(func_def_13,type,
nat_size: nat > nat ).
tff(func_def_14,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_15,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_16,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_17,type,
char1: ( nibble * nibble ) > char ).
tff(func_def_18,type,
char_case:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char ) > X0 ) ).
tff(func_def_19,type,
char_rec:
!>[X0: $tType] : ( ( fun(nibble,fun(nibble,X0)) * char ) > X0 ) ).
tff(func_def_20,type,
char_size: char > nat ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_25,type,
sK0: state ).
tff(func_def_26,type,
sK1: state ).
tff(func_def_27,type,
sK2: state ).
tff(pred_def_1,type,
enum:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_HOL_Oequal:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
semigroup:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > $o ) ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
type_definition:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X1,X0) * fun(X1,bool) ) > $o ) ).
tff(pred_def_19,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_20,type,
pp: bool > $o ).
tff(f1,axiom,
( hoare_531836380gleton
<=> ? [X3: state,X4: state] : ( X3 != X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
tff(f139,axiom,
hoare_531836380gleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f140,conjecture,
! [X0: state] :
? [X1: state] : ( X1 != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f141,negated_conjecture,
~ ! [X0: state] :
? [X1: state] : ( X1 != X0 ),
inference(negated_conjecture,[status(cth)],[f140]) ).
tff(f142,plain,
( hoare_531836380gleton
<=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
inference(rectify,[],[f1]) ).
tff(f143,plain,
( hoare_531836380gleton
=> ? [X0: state,X1: state] : ( X0 != X1 ) ),
inference(unused_predicate_definition_removal,[],[f142]) ).
tff(f144,plain,
? [X0: state] :
! [X1: state] : ( X0 = X1 ),
inference(ennf_transformation,[],[f141]) ).
tff(f145,plain,
( ? [X0: state,X1: state] : ( X0 != X1 )
| ~ hoare_531836380gleton ),
inference(ennf_transformation,[],[f143]) ).
tff(f146,plain,
! [X1: state] : ( sK0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f144]) ).
tff(f147,plain,
( ( sK1 != sK2 )
| ~ hoare_531836380gleton ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f145]) ).
tff(f148,plain,
hoare_531836380gleton,
inference(cnf_transformation,[],[f139]) ).
tff(f149,plain,
! [X1: state] : ( sK0 = X1 ),
inference(cnf_transformation,[],[f146]) ).
tff(f150,plain,
( ( sK1 != sK2 )
| ~ hoare_531836380gleton ),
inference(cnf_transformation,[],[f147]) ).
tff(f151,plain,
! [X0: state,X1: state] : ( X0 = X1 ),
inference(superposition,[],[f149,f149]) ).
tff(f154,plain,
~ hoare_531836380gleton,
inference(forward_subsumption_resolution,[],[f150,f151]) ).
tff(f155,plain,
$false,
inference(forward_subsumption_resolution,[],[f154,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW469_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:00:55 UTC 2026
% 0.08/0.19 % 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
% 0.19/1.14 % (3978438)Detected formulas, will run a generic FOF schedule.
% 0.19/1.14 % (3978447)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2175754654:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.14 % (3978447)First to succeed.
% 0.19/1.14 % (3978447)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3978438"
% 0.19/1.14 % (3978443)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=1576188779:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.14 % (3978448)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1993407906:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.14 % (3978446)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2652083787:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.14 % (3978444)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=4065305602:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.14 % (3978445)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=2827160897:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.14 % (3978449)dis-21_1_sil=8000:lcm=predicate:random_seed=3415407948: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)
% 0.19/1.14 % (3978446)Also succeeded, but the first one will report.
% 0.19/1.14 % (3978445)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.14 % (3978448)Also succeeded, but the first one will report.
% 0.19/1.14 % (3978449)Instruction limit reached!
% 0.19/1.14 % (3978449)------------------------------
% 0.19/1.14 % (3978449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.14 % (3978449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.14 % (3978449)CaDiCaL version: 2.1.3
% 0.19/1.14 % (3978449)Termination reason: Instruction limit
% 0.19/1.14 % (3978449)Termination phase: Saturation
% 0.19/1.14 % (3978449)Time elapsed: 0.059 s
% 0.19/1.14 % (3978449)Peak memory usage: 89 MB
% 0.19/1.14 % (3978449)Instructions burned: 131 (million)
% 0.19/1.14 % (3978447)Refutation found. Thanks to Tanya!
% 0.19/1.14 % SZS status Theorem for theBenchmark
% 0.19/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.14 % (3978447)------------------------------
% 0.19/1.14 % (3978447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.14 % (3978447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.14 % (3978447)CaDiCaL version: 2.1.3
% 0.19/1.14 % (3978447)Termination reason: Refutation
% 0.19/1.14 % (3978447)Time elapsed: 0.001 s
% 0.19/1.14 % (3978447)Peak memory usage: 88 MB
% 0.19/1.14 % (3978447)Instructions burned: 1 (million)
% 0.19/1.14 % (3978447)------------------------------
% 0.19/1.14 % (3978447)------------------------------
% 0.19/1.14 % (3978438)Success in time 0.273 s
% 0.19/1.14 % Vampire exiting
%------------------------------------------------------------------------------