%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n011.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 08:50:23 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% 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 : 249 ( 103 equ; 12 cnn)
% Maximal formula atoms : 2 ( 5 avg)
% Number of connectives : 247 ( 55 ~; 42 |; 37 &; 108 @)
% ( 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 : 60 ( 0 sgn 16 !; 5 ?; 60 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
db1:
!>[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] :
( ( ( X3 = X2 )
& ~ X0 )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd) ).
thf(f3,conjecture,
! [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
= X1 )
& ( ( if @ $true @ X0 @ X1 )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f4,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
= 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] :
( ( ( X3 = X2 )
& ~ X0 )
| ( ( X3 = X1 )
& X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
= X1 )
& ( ( if @ $true @ X0 @ X1 )
= X0 ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
= X1 )
& ( ( if @ $true @ X0 @ X1 )
= X0 ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
? [X0: $i,X1: $i] :
( ( ( if @ $false @ X0 @ X1 )
!= X1 )
| ( ( if @ $true @ X0 @ X1 )
!= X0 ) ),
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)],[f12]) ).
thf(f14,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( sK1
!= ( if @ $false @ sK0 @ sK1 ) )
| ( sK0
!= ( if @ $true @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( ( sK1
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
@ $false
@ sK0
@ sK1 ) )
| ( sK0
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( Y0
& ( Y1 = Y3 ) )
| ( ~ Y0
& ( Y2 = Y3 ) ) ) )
@ $true
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f16,f15,f15]) ).
thf(f20,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( ~ $false
& ( sK1 = Y0 ) ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( $true
& ( sK1 = Y0 ) ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f20]) ).
thf(f22,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( $false
& ( sK0 = Y0 ) )
| ( sK1 = Y0 ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f21]) ).
thf(f23,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] :
( $false
| ( sK1 = Y0 ) ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f22]) ).
thf(f24,plain,
( ( sK1
!= ( eps
@ ^ [Y0: $i] : ( sK1 = Y0 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f23]) ).
thf(f25,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( ~ $true
& ( sK1 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| ( $false
& ( sK1 = Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f25]) ).
thf(f27,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( ( $true
& ( sK0 = Y0 ) )
| $false ) ) ) ),
inference(boolean_simplification,[],[f26]) ).
thf(f28,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] :
( $true
& ( sK0 = Y0 ) ) ) ) ),
inference(boolean_simplification,[],[f27]) ).
thf(f29,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ),
inference(boolean_simplification,[],[f28]) ).
thf(f30,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| ( sK0
!= ( eps @ ( (=) @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f32,definition,
( spl2_1
<=> ( sK0
= ( eps @ ( (=) @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f34,plain,
( ( sK0
!= ( eps @ ( (=) @ sK0 ) ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,definition,
( spl2_2
<=> ( sK1
= ( eps @ ( (=) @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f38,plain,
( ( sK1
!= ( eps @ ( (=) @ sK1 ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f30,f36,f32]) ).
thf(f47,plain,
! [X0: $i] :
( ( eps @ ( (=) @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f14]) ).
thf(f87,plain,
( ( sK0 != sK0 )
| spl2_1 ),
inference(constrained_superposition,[],[f34,f47]) ).
thf(f91,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f92,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f93,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f38,f47]) ).
thf(f94,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
spl2_1,
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
spl2_2,
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s4]) ).
thf(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:13:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25 % (381154)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (381163)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3951354006:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (381163)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (381163) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-381154-381163"...
% 0.07/0.25 % (381160)% WARNING: option uhcvi not known.
% 0.07/0.25 % (381163)...printing done.
% 0.07/0.25 % (381163)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (381163)------------------------------
% 0.07/0.25 % (381163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (381163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (381163)CaDiCaL version: 2.1.3
% 0.07/0.25 % (381163)Termination reason: Refutation
% 0.07/0.25 % (381163)Time elapsed: 0.003 s
% 0.07/0.25 % (381163)Peak memory usage: 12 MB
% 0.07/0.25 % (381163)Instructions burned: 5 (million)
% 0.07/0.25 % (381154)Success in time 0.032 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------