%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN057^5 : 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 08:41:39 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 433 ( 117 equ; 0 cnn)
% Maximal formula atoms : 13 ( 10 avg)
% Number of connectives : 374 ( 86 ~; 51 |; 54 &; 151 @)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 44 !; 16 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cI: $i > $o ).
thf(func_def_1,type,
cJ: $i > $o ).
thf(func_def_2,type,
cH: $i > $o ).
thf(func_def_3,type,
cG: $i > $o ).
thf(func_def_4,type,
cF: $i > $o ).
thf(f1,conjecture,
( ( ( ? [X0: $i] :
( ( cH @ X0 )
& ~ ( cG @ X0 ) )
=> ! [X0: $i] :
( ( cI @ X0 )
=> ~ ( cH @ X0 ) ) )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) )
& ! [X0: $i] :
( ( ( cI @ X0 )
& ( cJ @ X0 ) )
=> ( cF @ X0 ) )
& ? [X0: $i] :
( ( cF @ X0 )
& ~ ( cG @ X0 ) ) )
=> ! [X0: $i] :
( ( cJ @ X0 )
=> ~ ( cI @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL27) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] :
( ( cH @ X0 )
& ~ ( cG @ X0 ) )
=> ! [X0: $i] :
( ( cI @ X0 )
=> ~ ( cH @ X0 ) ) )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( cH @ X0 ) )
& ! [X0: $i] :
( ( ( cI @ X0 )
& ( cJ @ X0 ) )
=> ( cF @ X0 ) )
& ? [X0: $i] :
( ( cF @ X0 )
& ~ ( cG @ X0 ) ) )
=> ! [X0: $i] :
( ( cJ @ X0 )
=> ~ ( cI @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ? [X0: $i] :
( ( cH @ X0 )
& ~ ( cG @ X0 ) )
=> ! [X1: $i] :
( ( cI @ X1 )
=> ~ ( cH @ X1 ) ) )
& ! [X2: $i] :
( ( cF @ X2 )
=> ( cH @ X2 ) )
& ! [X3: $i] :
( ( ( cI @ X3 )
& ( cJ @ X3 ) )
=> ( cF @ X3 ) )
& ? [X4: $i] :
( ( cF @ X4 )
& ~ ( cG @ X4 ) ) )
=> ! [X5: $i] :
( ( cJ @ X5 )
=> ~ ( cI @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
( ( ( cH @ X0 )
= $true )
& ( ( cG @ X0 )
!= $true ) )
=> ! [X1: $i] :
( ( ( cI @ X1 )
= $true )
=> ( ( cH @ X1 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( cF @ X2 )
= $true )
=> ( ( cH @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( ( cI @ X3 )
= $true )
& ( ( cJ @ X3 )
= $true ) )
=> ( ( cF @ X3 )
= $true ) )
& ? [X4: $i] :
( ( ( cF @ X4 )
= $true )
& ( ( cG @ X4 )
!= $true ) ) )
=> ! [X5: $i] :
( ( ( cJ @ X5 )
= $true )
=> ( ( cI @ X5 )
!= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ( ? [X0: $i] :
( ( ( cG @ X0 )
!= $true )
& ( ( cH @ X0 )
= $true ) )
=> ! [X1: $i] :
( ( ( cI @ X1 )
= $true )
=> ( ( cH @ X1 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( cF @ X2 )
= $true )
=> ( ( cH @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( ( cI @ X3 )
= $true )
& ( ( cJ @ X3 )
= $true ) )
=> ( ( cF @ X3 )
= $true ) )
& ? [X4: $i] :
( ( ( cG @ X4 )
!= $true )
& ( ( cF @ X4 )
= $true ) ) )
=> ! [X5: $i] :
( ( ( cJ @ X5 )
= $true )
=> ( ( cI @ X5 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ? [X5: $i] :
( ( ( cI @ X5 )
= $true )
& ( ( cJ @ X5 )
= $true ) )
& ( ! [X0: $i] :
( ( ( cG @ X0 )
= $true )
| ( ( cH @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cH @ X1 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( cH @ X2 )
= $true )
| ( ( cF @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( ( cF @ X3 )
= $true )
| ( ( cI @ X3 )
!= $true )
| ( ( cJ @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( ( cG @ X4 )
!= $true )
& ( ( cF @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ! [X0: $i] :
( ( ( cG @ X0 )
= $true )
| ( ( cH @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cH @ X1 )
!= $true ) ) )
& ! [X3: $i] :
( ( ( cI @ X3 )
!= $true )
| ( ( cJ @ X3 )
!= $true )
| ( ( cF @ X3 )
= $true ) )
& ! [X2: $i] :
( ( ( cH @ X2 )
= $true )
| ( ( cF @ X2 )
!= $true ) )
& ? [X4: $i] :
( ( ( cG @ X4 )
!= $true )
& ( ( cF @ X4 )
= $true ) )
& ? [X5: $i] :
( ( ( cI @ X5 )
= $true )
& ( ( cJ @ X5 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ! [X0: $i] :
( ( ( cG @ X0 )
= $true )
| ( ( cH @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cH @ X1 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( cI @ X2 )
!= $true )
| ( ( cJ @ X2 )
!= $true )
| ( ( cF @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( cH @ X3 )
= $true )
| ( ( cF @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( ( cG @ X4 )
!= $true )
& ( ( cF @ X4 )
= $true ) )
& ? [X5: $i] :
( ( ( cI @ X5 )
= $true )
& ( ( cJ @ X5 )
= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ! [X0: $i] :
( ( ( cG @ X0 )
= $true )
| ( ( cH @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cH @ X1 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( cI @ X2 )
!= $true )
| ( ( cJ @ X2 )
!= $true )
| ( ( cF @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( cH @ X3 )
= $true )
| ( ( cF @ X3 )
!= $true ) )
& ( ( cG @ sK0 )
!= $true )
& ( ( cF @ sK0 )
= $true )
& ( ( cI @ sK1 )
= $true )
& ( ( cJ @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0),skolemize(X5,sK1)],[f8]) ).
thf(f10,plain,
( ( cJ @ sK1 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( cI @ sK1 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( cF @ sK0 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( cG @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X3: $i] :
( ( ( cF @ X3 )
!= $true )
| ( ( cH @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X2: $i] :
( ( ( cJ @ X2 )
!= $true )
| ( ( cF @ X2 )
= $true )
| ( ( cI @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cG @ X0 )
= $true )
| ( ( cH @ X1 )
!= $true )
| ( ( cH @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,definition,
( spl2_1
<=> ! [X0: $i] :
( ( ( cG @ X0 )
= $true )
| ( ( cH @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f21,plain,
( ! [X0: $i] :
( ( ( cH @ X0 )
!= $true )
| ( ( cG @ X0 )
= $true ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f23,definition,
( spl2_2
<=> ! [X1: $i] :
( ( ( cI @ X1 )
!= $true )
| ( ( cH @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f24,plain,
( ! [X1: $i] :
( ( ( cH @ X1 )
!= $true )
| ( ( cI @ X1 )
!= $true ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f16,f23,f20]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
= ( cH @ sK0 ) ) ),
inference(constrained_superposition,[],[f14,f12]) ).
thf(f27,plain,
( $true
= ( cH @ sK0 ) ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f30,plain,
( ( ( cI @ sK1 )
!= $true )
| ( $true != $true )
| ( ( cF @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f15,f10]) ).
thf(f31,plain,
( ( ( cF @ sK1 )
= $true )
| ( ( cI @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( ( cF @ sK1 )
= $true ),
inference(forward_subsumption_resolution,[],[f31,f11]) ).
thf(f33,plain,
( ( ( cH @ sK1 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f14,f32]) ).
thf(f34,plain,
( ( cH @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( ( ( cI @ sK1 )
!= $true )
| ( $true != $true )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f24,f34]) ).
thf(f36,plain,
( ( ( cI @ sK1 )
!= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f36,f11]) ).
thf(f38,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f37]) ).
thf(f40,plain,
( ( ( cG @ sK0 )
= $true )
| ( $true != $true )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f21,f27]) ).
thf(f41,plain,
( ( ( cG @ sK0 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f43,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f41,f13]) ).
thf(f44,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f43]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f45,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN057^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:15:35 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.20/0.28 % (1238217)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1238227)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=891469853:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1238227) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1238217-1238227"...
% 0.20/0.28 % (1238227)...printing done.
% 0.20/0.28 % (1238227)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1238227)------------------------------
% 0.20/0.28 % (1238227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1238227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1238227)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1238227)Termination reason: Refutation
% 0.20/0.28 % (1238227)Time elapsed: 0.002 s
% 0.20/0.28 % (1238227)Peak memory usage: 13 MB
% 0.20/0.28 % (1238227)Instructions burned: 4 (million)
% 0.20/0.28 % (1238217)Success in time 0.027 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------