%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO541^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:48:23 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 169 ( 104 equ; 10 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 243 ( 51 ~; 44 |; 37 &; 106 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 5 con; 0-4 aty)
% Number of variables : 62 ( 0 sgn 16 !; 5 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK0: $i > $i ).
thf(func_def_15,type,
sK1: $i > $i ).
thf(f1,axiom,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxii) ).
thf(f2,axiom,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( ~ X0
& ( X3 = X2 ) )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifd) ).
thf(f3,conjecture,
! [X0: $i > $i,X1: $i > $i] :
( ( X0
= ( if @ $true @ X0 @ X1 ) )
& ( ( if @ $false @ X0 @ X1 )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( X0
= ( if @ $true @ X0 @ X1 ) )
& ( ( if @ $false @ X0 @ X1 )
= X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( ~ X0
& ( X3 = X2 ) )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( X0
= ( if @ $true @ X0 @ X1 ) )
& ( ( if @ $false @ X0 @ X1 )
= X1 ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X0: $i > $i,X1: $i > $i] :
( ( ( if @ $true @ X0 @ X1 )
= X0 )
& ( ( if @ $false @ X0 @ X1 )
= X1 ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] : ( X0 @ X1 )
=> ( X0 @ ( epsii @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
! [X0: ( $i > $i ) > $o] :
( ? [X1: $i > $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X0: $i > $i,X1: $i > $i] :
( ( ( if @ $false @ X0 @ X1 )
!= X1 )
| ( ( if @ $true @ X0 @ X1 )
!= X0 ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: ( $i > $i ) > $o] :
( ! [X1: $i > $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( sK1
!= ( if @ $false @ sK0 @ sK1 ) )
| ( sK0
!= ( if @ $true @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
thf(f14,plain,
( ( sK1
!= ( if @ $false @ sK0 @ sK1 ) )
| ( sK0
!= ( if @ $true @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f15,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
! [X0: ( $i > $i ) > $o,X1: $i > $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsii @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( ( sK0
!= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ $true
@ sK0
@ sK1 ) )
| ( sK1
!= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ( Y2 = Y3 )
& ~ Y0 ) ) )
@ $false
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f14,f15,f15]) ).
thf(f20,plain,
( ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& ~ $false ) ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& ~ $true ) ) )
!= sK0 ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& ~ $true ) ) )
!= sK0 )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& $true ) ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f22,plain,
( ( sK0
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& $false ) ) ) )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& $true ) ) ) ) ),
inference(boolean_simplification,[],[f21]) ).
thf(f23,plain,
( ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( ( sK1 = Y0 )
& $true ) ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( $true
& ( sK0 = Y0 ) )
| $false ) )
!= sK0 ) ),
inference(boolean_simplification,[],[f22]) ).
thf(f24,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( ( $true
& ( sK0 = Y0 ) )
| $false ) )
!= sK0 )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( sK1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f23]) ).
thf(f25,plain,
( ( ( epsii
@ ^ [Y0: $i > $i] :
( $true
& ( sK0 = Y0 ) ) )
!= sK0 )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( sK1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f24]) ).
thf(f26,plain,
( ( sK0
!= ( epsii
@ ^ [Y0: $i > $i] : ( sK0 = Y0 ) ) )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( sK1 = Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f25]) ).
thf(f27,plain,
( ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) )
| ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( sK1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
( ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( $false
| ( sK1 = Y0 ) ) ) )
| ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) ) ),
inference(boolean_simplification,[],[f27]) ).
thf(f29,plain,
( ( sK1
!= ( epsii
@ ^ [Y0: $i > $i] : ( sK1 = Y0 ) ) )
| ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) ) ),
inference(boolean_simplification,[],[f28]) ).
thf(f30,plain,
( ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) )
| ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f32,definition,
( spl2_1
<=> ( sK1
= ( epsii @ ( (=) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f34,plain,
( ( sK1
!= ( epsii @ ( (=) @ sK1 ) ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,definition,
( spl2_2
<=> ( sK0
= ( epsii @ ( (=) @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f38,plain,
( ( sK0
!= ( epsii @ ( (=) @ sK0 ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f30,f36,f32]) ).
thf(f41,plain,
! [X0: $i > $i] :
( ( epsii @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f16]) ).
thf(f53,plain,
( ( sK1 != sK1 )
| spl2_1 ),
inference(constrained_superposition,[],[f34,f41]) ).
thf(f54,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f55,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f54]) ).
thf(f56,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f38,f41]) ).
thf(f57,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f56]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f58,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO541^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:18:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 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
% 0.21/0.27 % (640688)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (640693)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3086084481:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (640693) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-640688-640693"...
% 0.21/0.27 % (640693)...printing done.
% 0.21/0.27 % (640693)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (640693)------------------------------
% 0.21/0.27 % (640693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (640693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (640693)CaDiCaL version: 2.1.3
% 0.21/0.27 % (640693)Termination reason: Refutation
% 0.21/0.27 % (640693)Time elapsed: 0.002 s
% 0.21/0.27 % (640693)Peak memory usage: 13 MB
% 0.21/0.27 % (640693)Instructions burned: 5 (million)
% 0.21/0.27 % (640688)Success in time 0.032 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------