%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:48:22 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 243 ( 101 equ; 10 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 252 ( 61 ~; 42 |; 32 &; 112 @)
% ( 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 : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 64 ( 0 sgn 16 !; 7 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
if: $o > $i > $i > $i ).
thf(func_def_5,type,
vOR: $o > $o > $o ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
( if
= ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( X0
& ( X3 = X1 ) )
| ( ~ X0
& ( X3 = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd) ).
thf(f3,conjecture,
! [X1: $i,X0: $i] :
( ( X1
= ( if @ $false @ X0 @ X1 ) )
& ( ( if @ $true @ X0 @ X1 )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X1
= ( if @ $false @ X0 @ X1 ) )
& ( ( if @ $true @ X0 @ X1 )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( if
= ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( X0
& ( X3 = X1 ) )
| ( ~ X0
& ( X3 = X2 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i,X1: $i] :
( ( X0
= ( if @ $false @ X1 @ X0 ) )
& ( ( if @ $true @ X1 @ X0 )
= X1 ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $true @ X1 @ X0 )
= X1 )
& ( ( if @ $false @ X1 @ X0 )
= X0 ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X1: $i,X0: $i] :
( ( ( if @ $false @ X1 @ X0 )
!= X0 )
| ( ( if @ $true @ X1 @ X0 )
!= X1 ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
? [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
!= X1 )
| ( ( if @ $true @ X0 @ X1 )
!= X0 ) ),
inference(rectify,[],[f11]) ).
thf(f14,plain,
( ( ( if @ $false @ sK0 @ sK1 )
!= sK1 )
| ( ( if @ $true @ sK0 @ sK1 )
!= sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
thf(f15,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( ( if @ $false @ sK0 @ sK1 )
!= sK1 )
| ( ( if @ $true @ sK0 @ sK1 )
!= sK0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( ( sK0
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ $true
@ sK0
@ sK1 ) )
| ( ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ $false
@ sK0
@ sK1 )
!= sK1 ) ),
inference(definition_unfolding,[],[f16,f17,f17]) ).
thf(f21,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $true )
| ( ( sK0 = Y0 )
& $true ) ) )
!= sK0 )
| ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $false )
| ( ( sK0 = Y0 )
& $false ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $false )
| ( ( sK0 = Y0 )
& $false ) ) ) )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $true )
| ( sK0 = Y0 ) ) )
!= sK0 ) ),
inference(boolean_simplification,[],[f21]) ).
thf(f23,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $true )
| ( sK0 = Y0 ) ) )
!= sK0 )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $false )
| $false ) )
!= sK1 ) ),
inference(boolean_simplification,[],[f22]) ).
thf(f24,plain,
( ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& $false )
| ( sK0 = Y0 ) ) ) )
| ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $false )
| $false ) )
!= sK1 ) ),
inference(boolean_simplification,[],[f23]) ).
thf(f25,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( ( sK1 = Y0 )
& ~ $false )
| $false ) )
!= sK1 )
| ( ( eps
@ ^ [Y0: $i] :
( $false
| ( sK0 = Y0 ) ) )
!= sK0 ) ),
inference(boolean_simplification,[],[f24]) ).
thf(f26,plain,
( ( ( eps
@ ^ [Y0: $i] :
( $false
| ( sK0 = Y0 ) ) )
!= sK0 )
| ( ( eps
@ ^ [Y0: $i] :
( ( sK1 = Y0 )
& ~ $false ) )
!= sK1 ) ),
inference(boolean_simplification,[],[f25]) ).
thf(f27,plain,
( ( ( eps
@ ^ [Y0: $i] :
( ( sK1 = Y0 )
& ~ $false ) )
!= sK1 )
| ( ( eps
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
!= sK0 ) ),
inference(boolean_simplification,[],[f26]) ).
thf(f28,plain,
( ( ( eps @ ( (=) @ sK0 ) )
!= sK0 )
| ( ( eps
@ ^ [Y0: $i] :
( ( sK1 = Y0 )
& ~ $false ) )
!= sK1 ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( ( ( eps @ ( (=) @ sK0 ) )
!= sK0 )
| ( ( eps
@ ^ [Y0: $i] :
( ( sK1 = Y0 )
& $true ) )
!= sK1 ) ),
inference(boolean_simplification,[],[f28]) ).
thf(f30,plain,
( ( ( eps @ ( (=) @ sK0 ) )
!= sK0 )
| ( ( eps
@ ^ [Y0: $i] : ( sK1 = Y0 ) )
!= sK1 ) ),
inference(boolean_simplification,[],[f29]) ).
thf(f31,plain,
( ( ( eps @ ( (=) @ sK1 ) )
!= sK1 )
| ( ( eps @ ( (=) @ sK0 ) )
!= sK0 ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,definition,
( spl2_1
<=> ( ( eps @ ( (=) @ sK0 ) )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( eps @ ( (=) @ sK0 ) )
!= sK0 )
| spl2_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl2_2
<=> ( ( eps @ ( (=) @ sK1 ) )
= sK1 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f39,plain,
( ( ( eps @ ( (=) @ sK1 ) )
!= sK1 )
| spl2_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f31,f37,f33]) ).
thf(f41,plain,
! [X0: $i] :
( ( eps @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f15]) ).
thf(f52,plain,
( ( sK0 != sK0 )
| spl2_1 ),
inference(constrained_superposition,[],[f35,f41]) ).
thf(f53,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f53]) ).
thf(f55,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f39,f41]) ).
thf(f56,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n002.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 17:16:23 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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 % (1588201)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1588206)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1819030328:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1588206) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1588201-1588206"...
% 0.20/0.28 % (1588206)...printing done.
% 0.20/0.28 % (1588206)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 % (1588206)------------------------------
% 0.20/0.28 % (1588206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1588206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1588206)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1588206)Termination reason: Refutation
% 0.20/0.28 % (1588206)Time elapsed: 0.002 s
% 0.20/0.28 % (1588206)Peak memory usage: 13 MB
% 0.20/0.28 % (1588206)Instructions burned: 4 (million)
% 0.20/0.28 % (1588201)Success in time 0.035 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------