%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO104^5 : 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 : n009.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 08:46:37 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 20 unt; 0 typ; 16 def)
% Number of atoms : 530 ( 102 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 388 ( 81 ~; 86 |; 22 &; 184 @)
% ( 14 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 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 : 26 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 47 !; 9 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_9,type,
sF3: $o ).
thf(func_def_10,type,
sF4: $o ).
thf(func_def_11,type,
sF5: $o ).
thf(func_def_12,type,
sF6: $o ).
thf(func_def_13,type,
sF7: $i > $o ).
thf(func_def_14,type,
sF8: $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP2129) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X1: $i] : ( cQ @ X1 @ y )
& ! [X2: $i] : ( cP @ X2 @ y ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) )
<=> ( ! [X1: $i] :
( $true
= ( cQ @ X1 @ y ) )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) )
<~> ( ! [X1: $i] :
( $true
= ( cQ @ X1 @ y ) )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X1: $i] :
( $true
!= ( cQ @ X1 @ y ) )
| ? [X2: $i] :
( ( cP @ X2 @ y )
!= $true )
| ? [X0: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( cP @ X0 @ y )
!= $true ) ) )
& ( ( ! [X1: $i] :
( $true
= ( cQ @ X1 @ y ) )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) )
| ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ? [X1: $i] :
( $true
!= ( cQ @ X1 @ y ) )
| ? [X2: $i] :
( ( cP @ X2 @ y )
!= $true )
| ? [X0: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( cP @ X0 @ y )
!= $true ) ) )
& ( ( ! [X1: $i] :
( $true
= ( cQ @ X1 @ y ) )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) )
| ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ? [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ? [X1: $i] :
( ( cP @ X1 @ y )
!= $true )
| ? [X2: $i] :
( ( $true
!= ( cQ @ X2 @ y ) )
| ( ( cP @ X2 @ y )
!= $true ) ) )
& ( ( ! [X3: $i] :
( $true
= ( cQ @ X3 @ y ) )
& ! [X4: $i] :
( $true
= ( cP @ X4 @ y ) ) )
| ! [X5: $i] :
( ( $true
= ( cQ @ X5 @ y ) )
& ( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( $true
!= ( cQ @ sK0 @ y ) )
| ( $true
!= ( cP @ sK1 @ y ) )
| ( ( cQ @ sK2 @ y )
!= $true )
| ( ( cP @ sK2 @ y )
!= $true ) )
& ( ( ! [X3: $i] :
( $true
= ( cQ @ X3 @ y ) )
& ! [X4: $i] :
( $true
= ( cP @ X4 @ y ) ) )
| ! [X5: $i] :
( ( $true
= ( cQ @ X5 @ y ) )
& ( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cP @ X4 @ y ) )
| ( $true
= ( cP @ X5 @ y ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X3: $i,X5: $i] :
( ( $true
= ( cQ @ X3 @ y ) )
| ( $true
= ( cQ @ X5 @ y ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( $true
!= ( cQ @ sK0 @ y ) )
| ( $true
!= ( cP @ sK1 @ y ) )
| ( ( cQ @ sK2 @ y )
!= $true )
| ( ( cP @ sK2 @ y )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,definition,
( sF3
= ( cQ @ sK0 @ y ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f18,definition,
( sF4
= ( cP @ sK1 @ y ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f19,definition,
( sF5
= ( cQ @ sK2 @ y ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f20,plain,
( ( cQ @ sK2 @ y )
= sF5 ),
inference(reorient_equations,[],[f19]) ).
thf(f21,definition,
( sF6
= ( cP @ sK2 @ y ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f22,plain,
( ( cP @ sK2 @ y )
= sF6 ),
inference(reorient_equations,[],[f21]) ).
thf(f23,plain,
( ( $true != sF5 )
| ( $true != sF4 )
| ( $true != sF6 )
| ( sF3 != $true ) ),
inference(definition_folding,[],[f14,f22,f20,f18,f17]) ).
thf(f24,definition,
! [X3: $i] :
( ( sF7 @ X3 )
= ( cQ @ X3 @ y ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f25,plain,
! [X3: $i,X5: $i] :
( ( ( sF7 @ X3 )
= $true )
| ( $true
= ( sF7 @ X5 ) ) ),
inference(definition_folding,[],[f13,f24,f24]) ).
thf(f26,definition,
! [X5: $i] :
( ( sF8 @ X5 )
= ( cP @ X5 @ y ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f29,plain,
! [X4: $i,X5: $i] :
( ( ( sF8 @ X5 )
= $true )
| ( $true
= ( sF8 @ X4 ) ) ),
inference(definition_folding,[],[f10,f26,f26]) ).
thf(f31,plain,
! [X5: $i] :
( ( ( sF8 @ X5 )
= $false )
| ( $true
= ( cP @ X5 @ y ) ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f33,plain,
( ( $true = sF5 )
| ( ( cQ @ sK2 @ y )
= $false ) ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f34,plain,
( ( sF3 = $true )
| ( $false
= ( cQ @ sK0 @ y ) ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f37,plain,
! [X3: $i] :
( ( ( sF7 @ X3 )
= $false )
| ( $true
= ( cQ @ X3 @ y ) ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f39,plain,
( ( $true = sF6 )
| ( ( cP @ sK2 @ y )
= $false ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f40,plain,
( ( $false
= ( cP @ sK1 @ y ) )
| ( $true = sF4 ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f43,definition,
( spl9_1
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f47,definition,
( spl9_2
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f51,definition,
( spl9_3
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f55,definition,
( spl9_4
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f58,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f23,f55,f51,f47,f43]) ).
thf(f60,definition,
( spl9_5
<=> ( ( cQ @ sK2 @ y )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f62,plain,
( ( ( cQ @ sK2 @ y )
= $false )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,plain,
( spl9_2
| spl9_5 ),
inference(avatar_split_clause,[],[f33,f60,f47]) ).
thf(f83,definition,
( spl9_10
<=> ( $false
= ( cQ @ sK0 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f85,plain,
( ( $false
= ( cQ @ sK0 @ y ) )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f86,plain,
( spl9_1
| spl9_10 ),
inference(avatar_split_clause,[],[f34,f83,f43]) ).
thf(f88,definition,
( spl9_11
<=> ! [X5: $i] :
( ( sF8 @ X5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f89,plain,
( ! [X5: $i] :
( ( sF8 @ X5 )
= $true )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f91,definition,
( spl9_12
<=> ! [X3: $i] :
( ( sF7 @ X3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition]) ).
thf(f92,plain,
( ! [X3: $i] :
( ( sF7 @ X3 )
= $true )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f94,plain,
( spl9_11
| spl9_11 ),
inference(avatar_split_clause,[],[f29,f88,f88]) ).
thf(f95,plain,
( spl9_12
| spl9_12 ),
inference(avatar_split_clause,[],[f25,f91,f91]) ).
thf(f97,definition,
( spl9_13
<=> ( ( cP @ sK2 @ y )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f99,plain,
( ( ( cP @ sK2 @ y )
= $false )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f97]) ).
thf(f100,plain,
( spl9_3
| spl9_13 ),
inference(avatar_split_clause,[],[f39,f97,f51]) ).
thf(f120,definition,
( spl9_18
<=> ( $false
= ( cP @ sK1 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition]) ).
thf(f122,plain,
( ( $false
= ( cP @ sK1 @ y ) )
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f123,plain,
( spl9_4
| spl9_18 ),
inference(avatar_split_clause,[],[f40,f120,f55]) ).
thf(f139,plain,
( ! [X5: $i] :
( ( $true = $false )
| ( $true
= ( cP @ X5 @ y ) ) )
| ~ spl9_11 ),
inference(forward_demodulation,[],[f31,f89]) ).
thf(f140,plain,
( ! [X5: $i] :
( $true
= ( cP @ X5 @ y ) )
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f141,plain,
( ! [X3: $i] :
( ( $true
= ( cQ @ X3 @ y ) )
| ( $true = $false ) )
| ~ spl9_12 ),
inference(forward_demodulation,[],[f37,f92]) ).
thf(f142,plain,
( ! [X3: $i] :
( $true
= ( cQ @ X3 @ y ) )
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f141]) ).
thf(f143,plain,
( ( $true = $false )
| ~ spl9_10
| ~ spl9_12 ),
inference(constrained_superposition,[],[f142,f85]) ).
thf(f147,plain,
( $false
| ~ spl9_10
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f143]) ).
thf(f148,plain,
( ~ spl9_10
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f147]) ).
thf(f156,plain,
( ( $true = $false )
| ~ spl9_11
| ~ spl9_13 ),
inference(forward_demodulation,[],[f99,f140]) ).
thf(f157,plain,
( $false
| ~ spl9_11
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f158,plain,
( ~ spl9_11
| ~ spl9_13 ),
inference(avatar_contradiction_clause,[],[f157]) ).
thf(f165,plain,
( ( $true = $false )
| ~ spl9_11
| ~ spl9_18 ),
inference(forward_demodulation,[],[f122,f140]) ).
thf(f166,plain,
( $false
| ~ spl9_11
| ~ spl9_18 ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f167,plain,
( ~ spl9_11
| ~ spl9_18 ),
inference(avatar_contradiction_clause,[],[f166]) ).
thf(f176,plain,
( ( $true = $false )
| ~ spl9_5
| ~ spl9_12 ),
inference(forward_demodulation,[],[f62,f142]) ).
thf(f177,plain,
( $false
| ~ spl9_5
| ~ spl9_12 ),
inference(trivial_inequality_removal,[],[f176]) ).
thf(f178,plain,
( ~ spl9_5
| ~ spl9_12 ),
inference(avatar_contradiction_clause,[],[f177]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
( spl9_2
| spl9_5 ),
inference(sat_conversion,[],[f63]) ).
cnf(s5,plain,
( spl9_1
| spl9_10 ),
inference(sat_conversion,[],[f86]) ).
cnf(s7,plain,
( spl9_11
| spl9_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s8,plain,
spl9_11,
inference(rat,[],[s7]) ).
cnf(s9,plain,
( spl9_12
| spl9_12 ),
inference(sat_conversion,[],[f95]) ).
cnf(s10,plain,
spl9_12,
inference(rat,[],[s9]) ).
cnf(s11,plain,
( spl9_3
| spl9_13 ),
inference(sat_conversion,[],[f100]) ).
cnf(s14,plain,
( spl9_4
| spl9_18 ),
inference(sat_conversion,[],[f123]) ).
cnf(s17,plain,
( ~ spl9_10
| ~ spl9_12 ),
inference(sat_conversion,[],[f148]) ).
cnf(s20,plain,
( ~ spl9_11
| ~ spl9_13 ),
inference(sat_conversion,[],[f158]) ).
cnf(s23,plain,
( ~ spl9_11
| ~ spl9_18 ),
inference(sat_conversion,[],[f167]) ).
cnf(s27,plain,
( ~ spl9_5
| ~ spl9_12 ),
inference(sat_conversion,[],[f178]) ).
cnf(s28,plain,
~ spl9_5,
inference(rat,[],[s27,s10]) ).
cnf(s30,plain,
~ spl9_10,
inference(rat,[],[s17,s10]) ).
cnf(s32,plain,
~ spl9_18,
inference(rat,[],[s23,s8]) ).
cnf(s34,plain,
~ spl9_13,
inference(rat,[],[s20,s8]) ).
cnf(s35,plain,
spl9_4,
inference(rat,[],[s14,s32]) ).
cnf(s36,plain,
spl9_3,
inference(rat,[],[s11,s34]) ).
cnf(s37,plain,
spl9_1,
inference(rat,[],[s5,s30]) ).
cnf(s40,plain,
spl9_2,
inference(rat,[],[s2,s28]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s1,s35,s36,s40,s37]) ).
thf(f179,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO104^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.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 : Tue Sep 29 16:34:05 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (23313)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (23337)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (23337)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
% 0.20/0.28 % (23337)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1354035913:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (23337) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-23313-23337"...
% 0.20/0.28 % (23337)...printing done.
% 0.20/0.28 % (23337)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 % (23337)------------------------------
% 0.20/0.28 % (23337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (23337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (23337)CaDiCaL version: 2.1.3
% 0.20/0.28 % (23337)Termination reason: Refutation
% 0.20/0.28 % (23337)Time elapsed: 0.003 s
% 0.20/0.28 % (23337)Peak memory usage: 13 MB
% 0.20/0.28 % (23337)Instructions burned: 6 (million)
% 0.20/0.28 % (23313)Success in time 0.036 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------