%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO160^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:46:45 AM UTC 2026
% Result : Theorem 0.26s 0.36s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 323 ( 63 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 262 ( 65 ~; 69 |; 25 &; 86 @)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cR: $i > $o ).
thf(func_def_4,type,
cQ: $i > $o ).
thf(func_def_5,type,
cP: $i > $o ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ X0 ) )
& ( ! [X0: $i] : ( cQ @ X0 )
| ! [X0: $i] : ( cP @ X0 ) ) )
=> ( ( cR @ a )
& ( cR @ c )
& ( cR @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDISJ_THIRD) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ X0 ) )
& ( ! [X0: $i] : ( cQ @ X0 )
| ! [X0: $i] : ( cP @ X0 ) ) )
=> ( ( cR @ a )
& ( cR @ c )
& ( cR @ b ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cR @ X0 ) )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ X1 ) )
& ( ! [X2: $i] : ( cQ @ X2 )
| ! [X3: $i] : ( cP @ X3 ) ) )
=> ( ( cR @ a )
& ( cR @ c )
& ( cR @ b ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
=> ( $true
= ( cR @ X1 ) ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( cR @ X0 )
= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( $true
= ( cQ @ X2 ) ) ) )
=> ( ( ( cR @ c )
= $true )
& ( ( cR @ a )
= $true )
& ( ( cR @ b )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ( cR @ c )
!= $true )
| ( ( cR @ a )
!= $true )
| ( ( cR @ b )
!= $true ) )
& ! [X1: $i] :
( ( $true
!= ( cQ @ X1 ) )
| ( $true
= ( cR @ X1 ) ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( $true
= ( cQ @ X2 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i] :
( ( $true
!= ( cQ @ X1 ) )
| ( $true
= ( cR @ X1 ) ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( $true
= ( cQ @ X2 ) ) )
& ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( ( cR @ c )
!= $true )
| ( ( cR @ a )
!= $true )
| ( ( cR @ b )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X2: $i] :
( $true
= ( cQ @ X2 ) ) )
& ! [X3: $i] :
( ( $true
= ( cR @ X3 ) )
| ( $true
!= ( cP @ X3 ) ) )
& ( ( ( cR @ c )
!= $true )
| ( ( cR @ a )
!= $true )
| ( ( cR @ b )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cR @ b )
!= $true )
| ( ( cR @ a )
!= $true )
| ( ( cR @ c )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( $true
= ( cR @ X3 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( cQ @ X2 ) )
| ( ( cP @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cR @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,definition,
( spl0_1
<=> ( ( cR @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f17,plain,
( ( ( cR @ c )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl0_2
<=> ( ( cR @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( cR @ b )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f23,definition,
( spl0_3
<=> ( ( cR @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f25,plain,
( ( ( cR @ a )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f8,f23,f19,f15]) ).
thf(f28,definition,
( spl0_4
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f29,plain,
( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,definition,
( spl0_5
<=> ! [X2: $i] :
( $true
= ( cQ @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f32,plain,
( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f31,f28]) ).
thf(f34,plain,
( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f9,f29]) ).
thf(f35,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
( ( $true != $true )
| spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f17,f35]) ).
thf(f37,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f37]) ).
thf(f39,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 )
= $true ) )
| ~ spl0_5 ),
inference(constrained_superposition,[],[f11,f32]) ).
thf(f40,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ( $true != $true )
| spl0_1
| ~ spl0_5 ),
inference(constrained_superposition,[],[f17,f40]) ).
thf(f42,plain,
( $false
| spl0_1
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f44,plain,
( $false
| spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f21,f35]) ).
thf(f45,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f44]) ).
thf(f46,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f25,f35]) ).
thf(f47,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f46]) ).
thf(f48,plain,
( $false
| spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f25,f40]) ).
thf(f49,plain,
( spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f48]) ).
thf(f50,plain,
( $false
| spl0_2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f21,f40]) ).
thf(f51,plain,
( spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f33]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s6,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s7,plain,
( spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s8,plain,
( spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f51]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s2,s3,s4]) ).
cnf(s10,plain,
spl0_2,
inference(rat,[],[s2,s5,s8]) ).
cnf(s11,plain,
~ spl0_3,
inference(rat,[],[s1,s9,s10]) ).
cnf(s12,plain,
~ spl0_5,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
~ spl0_4,
inference(rat,[],[s6,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s12,s13]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO160^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n026.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:38:42 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.36 % (834304)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.36 % (834311)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1127195264:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.36 % (834315)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.36 % (834315)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
% 0.26/0.36 % (834311) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-834304-834311"...
% 0.26/0.36 % (834311)...printing done.
% 0.26/0.36 % (834311)Refutation found. Thanks to Tanya!
% 0.26/0.36 % SZS status Theorem for theBenchmark
% 0.26/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (834311)------------------------------
% 0.26/0.36 % (834311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (834311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (834311)CaDiCaL version: 2.1.3
% 0.26/0.36 % (834311)Termination reason: Refutation
% 0.26/0.36 % (834311)Time elapsed: 0.003 s
% 0.26/0.36 % (834311)Peak memory usage: 13 MB
% 0.26/0.36 % (834311)Instructions burned: 3 (million)
% 0.26/0.36 % (834304)Success in time 0.032 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------