%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO378^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:47:33 AM UTC 2026
% Result : Theorem 0.12s 0.26s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 72 equ; 9 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 130 ( 12 ~; 6 |; 20 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 15 usr; 5 con; 0-4 aty)
% ( 0 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 33 ^; 16 !; 8 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQDP0: $i > $o ).
thf(func_def_2,type,
cQDP1: ( $i > $o ) > $o ).
thf(func_def_3,type,
cQDP2: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK0: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_15,type,
sK1: ( ( $i > $o ) > $o ) > $i ).
thf(func_def_16,type,
sK2: ( $i > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i] : ( X0 = c ) )
= cQDP0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP0_def) ).
thf(f2,axiom,
( cQDP1
= ( ^ [X0: $i > $o] :
( ( X0 = cQDP0 )
& ? [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP1_def) ).
thf(f3,axiom,
( ( ^ [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
& ( X0 = cQDP1 ) ) )
= cQDP2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDP2_def) ).
thf(f4,conjecture,
? [X0: ( $i > $o ) > $o] : ( cQDP2 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cQDTHM2) ).
thf(f5,negated_conjecture,
~ ? [X0: ( $i > $o ) > $o] : ( cQDP2 @ X0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f7,plain,
~ ? [X0: ( $i > $o ) > $o] : ( cQDP2 @ X0 ),
inference(rectify,[],[f5]) ).
thf(f8,plain,
~ ? [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( cQDP1
= ( ^ [X0: $i > $o] :
( ( X0 = cQDP0 )
& ? [X1: $i] : ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( cQDP0 = Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
& ( X0 = cQDP1 ) ) )
= cQDP2 ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( cQDP1 = Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
!= $true ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f15,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( cQDP1 = Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( cQDP0 = Y0 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 ) ) ) ),
inference(definition_unfolding,[],[f17,f15]) ).
thf(f21,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( ( ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( ( ^ [Y2: $i] : ( c = Y2 ) )
= Y1 ) ) )
= Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f16,f20]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( ( ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( ( ^ [Y2: $i] : ( c = Y2 ) )
= Y1 ) ) )
= Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) )
@ X0 )
!= $true ),
inference(definition_unfolding,[],[f14,f21]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > $o] :
( $true
!= ( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
= X0 )
& ( ?? @ ( $i > $o ) @ X0 ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > $o] :
( ( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
= X0 )
= $false )
| ( $false
= ( ?? @ ( $i > $o ) @ X0 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > $o] :
( ( $false
= ( ?? @ ( $i > $o ) @ X0 ) )
| ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
!= X0 ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f29,plain,
! [X0: $i > $o] :
( $false
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) )
@ X0 ) ),
inference(equality_resolution,[],[f26]) ).
thf(f43,plain,
! [X0: $i > $o] :
( $false
= ( ( ?? @ $i @ X0 )
& ( ( (=) @ c )
= X0 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f44,plain,
! [X0: $i > $o] :
( ( $false
= ( ( (=) @ c )
= X0 ) )
| ( $false
= ( ?? @ $i @ X0 ) ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X0: $i > $o] :
( ( ( (=) @ c )
!= X0 )
| ( $false
= ( ?? @ $i @ X0 ) ) ),
inference(equality_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X0: $i > $o,X1: $i] :
( ( ( (=) @ c )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f49,plain,
! [X0: $i] :
( $false
= ( c = X0 ) ),
inference(equality_resolution,[],[f46]) ).
thf(f56,plain,
! [X0: $i] : ( c != X0 ),
inference(equality_proxy_clausification,[],[f49]) ).
thf(f58,plain,
$false,
inference(equality_resolution,[],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO378^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n020.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 16:50:35 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.23 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
% 0.12/0.26 % (1298796)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.26 % (1298805)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3408161876:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.12/0.26 % (1298805) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1298796-1298805"...
% 0.12/0.26 % (1298805)...printing done.
% 0.12/0.26 % (1298805)Refutation found. Thanks to Tanya!
% 0.12/0.26 % SZS status Theorem for theBenchmark
% 0.12/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.26 % (1298805)------------------------------
% 0.12/0.26 % (1298805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.26 % (1298805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.26 % (1298805)CaDiCaL version: 2.1.3
% 0.12/0.26 % (1298805)Termination reason: Refutation
% 0.12/0.26 % (1298805)Time elapsed: 0.002 s
% 0.12/0.26 % (1298805)Peak memory usage: 12 MB
% 0.12/0.26 % (1298805)Instructions burned: 3 (million)
% 0.12/0.26 % (1298796)Success in time 0.018 s
% 0.12/0.26 % Vampire exiting
%------------------------------------------------------------------------------