%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR153^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 07:47:13 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 253 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 213 ( 67 ~; 31 |; 11 &; 94 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 6 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 18 ^; 39 !; 4 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
num: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
brother_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_5,type,
sister_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f3,axiom,
( ( lSue_THFTYPE_i != lBill_THFTYPE_i )
& ( lSue_THFTYPE_i != lBob_THFTYPE_i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_002) ).
thf(f5,axiom,
lBob_THFTYPE_i != lBill_THFTYPE_i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_004) ).
thf(f6,conjecture,
? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f7,negated_conjecture,
~ ? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f10,plain,
( ( lSue_THFTYPE_i != lBill_THFTYPE_i )
& ( lSue_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( $true
= ( lSue_THFTYPE_i != lBill_THFTYPE_i ) )
& ( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ? [X0: $i > $i > $o] :
( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ~ ! [X1: $i,X2: $i] : ( X0 @ X1 @ X2 )
& ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
inference(rectify,[],[f7]) ).
thf(f13,plain,
~ ? [X0: $i > $i > $o] :
( ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
= $true )
& ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
& ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f18,plain,
lBob_THFTYPE_i != lBill_THFTYPE_i,
inference(rectify,[],[f5]) ).
thf(f19,plain,
( $true
= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f21,plain,
( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f26,plain,
( $true
= ( lBill_THFTYPE_i != lBob_THFTYPE_i ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
! [X0: $i > $i > $o] :
( ( $true
!= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) ) )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f40,plain,
! [X0: $i > $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) ) ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f41,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( X0 @ Y1 @ Y0 ) )
@ X1 ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( X0 @ Y0 @ X1 ) ) )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] : ( X0 @ Y0 @ X1 )
@ X2 )
= $true )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true )
| ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( ( X0 @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
!= $true )
| ( $true
= ( X0 @ X2 @ X1 ) )
| ( ( X0 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
!= $true ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f50,plain,
( ( lSue_THFTYPE_i = lBob_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f51,plain,
lSue_THFTYPE_i != lBob_THFTYPE_i,
inference(equality_proxy_clausification,[],[f50]) ).
thf(f54,plain,
( ( lBill_THFTYPE_i = lBob_THFTYPE_i )
= $false ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f55,plain,
lBill_THFTYPE_i != lBob_THFTYPE_i,
inference(equality_proxy_clausification,[],[f54]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ lSue_THFTYPE_i
@ lBob_THFTYPE_i ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ X2
@ X1 ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 != Y1 )
@ lBob_THFTYPE_i
@ lBill_THFTYPE_i ) ) ),
inference(primitive_instantiation,[],[f44]) ).
thf(f76,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 != X1 ) )
| ( $true
!= ( lBob_THFTYPE_i != lBill_THFTYPE_i ) )
| ( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
!= $true ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f77,plain,
! [X2: $i,X1: $i] :
( ( ( X2 = X1 )
= $false )
| ( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
!= $true )
| ( $true
!= ( lBob_THFTYPE_i != lBill_THFTYPE_i ) ) ),
inference(not_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( ( lSue_THFTYPE_i != lBob_THFTYPE_i )
!= $true )
| ( $true
!= ( lBob_THFTYPE_i != lBill_THFTYPE_i ) ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( lSue_THFTYPE_i = lBob_THFTYPE_i ) )
| ( X1 != X2 )
| ( $true
!= ( lBob_THFTYPE_i != lBill_THFTYPE_i ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X2: $i,X1: $i] :
( ( lSue_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 )
| ( $true
!= ( lBob_THFTYPE_i != lBill_THFTYPE_i ) ) ),
inference(equality_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( lBob_THFTYPE_i = lBill_THFTYPE_i ) )
| ( X1 != X2 )
| ( lSue_THFTYPE_i = lBob_THFTYPE_i ) ),
inference(not_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X1: $i] :
( ( lSue_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 )
| ( lBill_THFTYPE_i = lBob_THFTYPE_i ) ),
inference(equality_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X1: $i] :
( ( lBill_THFTYPE_i = lBob_THFTYPE_i )
| ( X1 != X2 ) ),
inference(forward_subsumption_resolution,[],[f82,f51]) ).
thf(f84,plain,
! [X2: $i,X1: $i] : ( X1 != X2 ),
inference(forward_subsumption_resolution,[],[f83,f55]) ).
thf(f85,plain,
$false,
inference(flex-flex_simplification,[],[f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR153^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:03:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.28 % (1615823)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (1615828)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1291811628:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.28 % (1615828) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1615823-1615828"...
% 0.23/0.28 % (1615828)...printing done.
% 0.23/0.28 % (1615828)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.28 % (1615828)------------------------------
% 0.23/0.28 % (1615828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (1615828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (1615828)CaDiCaL version: 2.1.3
% 0.23/0.28 % (1615828)Termination reason: Refutation
% 0.23/0.28 % (1615828)Time elapsed: 0.002 s
% 0.23/0.28 % (1615828)Peak memory usage: 12 MB
% 0.23/0.28 % (1615828)Instructions burned: 4 (million)
% 0.23/0.28 % (1615823)Success in time 0.03 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------