%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:46:25 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 50 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 279 ( 24 ~; 6 |; 0 &; 203 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 4 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 86 ( 70 ^; 16 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a: $i > $o ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_35,type,
sK1: $i > $i ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) )
= inot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f25,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f26,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f27,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f33,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f34,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f37,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f38,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f39,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f38]) ).
thf(f45,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f46,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f53,plain,
~ ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f54,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f56,plain,
ivalid @ ( iatom @ a ),
inference(rectify,[],[f22]) ).
thf(f57,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f59,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(flattening,[],[f54]) ).
thf(f66,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(cnf_transformation,[],[f57]) ).
thf(f71,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f72,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f39]) ).
thf(f73,plain,
( ( ivalid @ ( inot @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f75,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f80,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f81,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f85,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f89,plain,
( inot
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f75,f80,f71]) ).
thf(f97,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ),
inference(definition_unfolding,[],[f66,f85,f81]) ).
thf(f98,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ) ) ),
inference(definition_unfolding,[],[f73,f85,f89,f89,f81]) ).
thf(f99,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( $false
= ( irel @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( a @ Y0 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( ( ( irel @ X1 @ ( sK1 @ X1 ) )
=> ( a @ ( sK1 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK0 @ X1 ) )
| ( $false
= ( a @ ( sK1 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f111,plain,
( $true
= ( !! @ $i @ a ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f112,plain,
! [X1: $i] :
( ( a @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f111]) ).
thf(f114,plain,
( ( ( a @ ( sK1 @ sK0 ) )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f72,f109]) ).
thf(f115,plain,
( ( a @ ( sK1 @ sK0 ) )
= $false ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f117,plain,
$false = $true,
inference(forward_demodulation,[],[f115,f112]) ).
thf(f118,plain,
$false,
inference(trivial_inequality_removal,[],[f117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.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 16:27:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.30 % (2704442)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2704448)lrs+10_16_si=on:nwc=1.5:random_seed=4048090647:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2704449)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=900837279:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2704451)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1523657654:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2704450)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1100562764:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (2704447)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1013529094:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2704449)Instruction limit reached!
% 0.22/0.30 % (2704449)------------------------------
% 0.22/0.30 % (2704449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2704449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2704449)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2704449)Termination reason: Instruction limit
% 0.22/0.30 % (2704449)Termination phase: Saturation
% 0.22/0.30 % (2704449)Time elapsed: 0.002 s
% 0.22/0.30 % (2704449)Peak memory usage: 10 MB
% 0.22/0.30 % (2704449)Instructions burned: 3 (million)
% 0.22/0.30 % (2704448) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2704442-2704448"...
% 0.22/0.30 % (2704447) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2704442-2704447"...
% 0.22/0.30 % (2704448)...printing done.
% 0.22/0.30 % (2704447)...printing done.
% 0.22/0.30 % (2704448)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (2704448)------------------------------
% 0.22/0.30 % (2704448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2704448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2704448)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2704448)Termination reason: Refutation
% 0.22/0.30 % (2704448)Time elapsed: 0.005 s
% 0.22/0.30 % (2704448)Peak memory usage: 12 MB
% 0.22/0.30 % (2704448)Instructions burned: 6 (million)
% 0.22/0.30 % (2704442)Success in time 0.043 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------