%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET014^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Wed Sep 30 08:23:10 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 150 ( 52 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 168 ( 32 ~; 31 |; 16 &; 71 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(func_def_6,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_32_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( X1 @ X3 )
| ( X0 @ X3 ) )
=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X5: a] :
( ( ( X1 @ X5 )
| ( X2 @ X5 ) )
=> ( X0 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( ( X0 @ X4 )
= $true ) ) )
=> ! [X5: a] :
( ( ( $true
= ( X2 @ X5 ) )
| ( $true
= ( X1 @ X5 ) ) )
=> ( $true
= ( X0 @ X5 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( ( $true
= ( X2 @ X5 ) )
| ( $true
= ( X1 @ X5 ) ) )
& ( $true
!= ( X0 @ X5 ) ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
| ( ( X0 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X2: a > $o,X1: a > $o] :
( ? [X5: a] :
( ( ( $true
= ( X2 @ X5 ) )
| ( $true
= ( X1 @ X5 ) ) )
& ( $true
!= ( X0 @ X5 ) ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( $true
!= ( X2 @ X4 ) )
| ( ( X0 @ X4 )
= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) )
& ( ( X0 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
| ( $true
= ( X0 @ X5 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) )
& ( $true
!= ( sK0 @ sK3 ) )
& ! [X4: a] :
( ( $true
= ( sK0 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) )
& ! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
! [X5: a] :
( ( $true
!= ( sK1 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X4: a] :
( ( $true
!= ( sK2 @ X4 ) )
| ( $true
= ( sK0 @ X4 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
!= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( spl4_1
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f17,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f12,f19,f16]) ).
thf(f22,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f9,f20]) ).
thf(f23,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f23,f11]) ).
thf(f25,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f24]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f10,f17]) ).
thf(f27,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f28,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f27,f11]) ).
thf(f29,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f28]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f30,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET014^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:36:05 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (1052942)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1052952)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=693746466:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (1052952) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1052942-1052952"...
% 0.22/0.28 % (1052952)...printing done.
% 0.22/0.28 % (1052953)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (1052953)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (1052952)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1052952)------------------------------
% 0.22/0.28 % (1052952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1052952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1052952)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1052952)Termination reason: Refutation
% 0.22/0.28 % (1052952)Time elapsed: 0.001 s
% 0.22/0.28 % (1052952)Peak memory usage: 13 MB
% 0.22/0.28 % (1052952)Instructions burned: 2 (million)
% 0.22/0.28 % (1052942)Success in time 0.031 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------