%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO102^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:46:37 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 224 ( 58 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 234 ( 26 ~; 18 |; 28 &; 150 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 52 !; 9 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X0: $i] : ( cP @ X0 @ X0 )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X2 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ! [X3: $i,X5: $i,X4: $i] :
( ( ( cP @ X4 @ X5 )
& ( cP @ X3 @ X4 ) )
=> ( cP @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM101) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] : ( cP @ X0 @ X0 )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X2 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ! [X3: $i,X5: $i,X4: $i] :
( ( ( cP @ X4 @ X5 )
& ( cP @ X3 @ X4 ) )
=> ( cP @ X3 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] : ( cP @ X0 @ X0 )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X2 @ X1 )
& ( cP @ X3 @ X1 ) )
=> ( cP @ X2 @ X3 ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X6 @ X5 )
& ( cP @ X4 @ X6 ) )
=> ( cP @ X4 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X1: $i,X2: $i,X3: $i] :
( ( ( ( cP @ X2 @ X1 )
= $true )
& ( ( cP @ X3 @ X1 )
= $true ) )
=> ( $true
= ( cP @ X2 @ X3 ) ) )
& ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true ) )
=> ! [X4: $i,X6: $i,X5: $i] :
( ( ( ( cP @ X4 @ X6 )
= $true )
& ( ( cP @ X6 @ X5 )
= $true ) )
=> ( ( cP @ X4 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X4: $i,X6: $i,X5: $i] :
( ( ( cP @ X4 @ X5 )
!= $true )
& ( ( cP @ X4 @ X6 )
= $true )
& ( ( cP @ X6 @ X5 )
= $true ) )
& ! [X1: $i,X2: $i,X3: $i] :
( ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X2 @ X1 )
!= $true )
| ( ( cP @ X3 @ X1 )
!= $true ) )
& ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X2 @ X1 )
!= $true )
| ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X3 @ X1 )
!= $true ) )
& ? [X5: $i,X6: $i,X4: $i] :
( ( ( cP @ X4 @ X6 )
= $true )
& ( ( cP @ X6 @ X5 )
= $true )
& ( ( cP @ X4 @ X5 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X2 @ X1 )
!= $true )
| ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X3 @ X1 )
!= $true ) )
& ? [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X6 @ X5 )
= $true )
& ( ( cP @ X5 @ X4 )
= $true )
& ( ( cP @ X6 @ X4 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X2 @ X1 )
!= $true )
| ( $true
= ( cP @ X2 @ X3 ) )
| ( ( cP @ X3 @ X1 )
!= $true ) )
& ( $true
= ( cP @ sK2 @ sK1 ) )
& ( $true
= ( cP @ sK1 @ sK0 ) )
& ( $true
!= ( cP @ sK2 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X4,sK0),skolemize(X5,sK1),skolemize(X6,sK2)],[f7]) ).
thf(f9,plain,
( $true
!= ( cP @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( cP @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( cP @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( cP @ X3 @ X1 )
!= $true )
| ( ( cP @ X2 @ X1 )
!= $true )
| ( $true
= ( cP @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( cP @ X0 @ sK0 )
!= $true )
| ( ( cP @ X0 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f12,f10]) ).
thf(f19,plain,
! [X0: $i] :
( ( ( cP @ X0 @ sK0 )
!= $true )
| ( ( cP @ X0 @ sK1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f22,plain,
( ( $true != $true )
| ( ( cP @ sK0 @ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f19,f13]) ).
thf(f24,plain,
( ( cP @ sK0 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f25,plain,
! [X0: $i] :
( ( ( cP @ X0 @ sK0 )
= $true )
| ( $true != $true )
| ( ( cP @ X0 @ sK1 )
!= $true ) ),
inference(constrained_superposition,[],[f12,f24]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( cP @ X0 @ sK1 )
!= $true )
| ( ( cP @ X0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f39,plain,
( ( $true
= ( cP @ sK2 @ sK0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f26,f11]) ).
thf(f40,plain,
( $true
= ( cP @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f43,plain,
$false,
inference(forward_subsumption_resolution,[],[f40,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO102^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:36:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.28 % (824571)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (824586)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1654721411:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (824586) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-824571-824586"...
% 0.21/0.28 % (824586)...printing done.
% 0.21/0.28 % (824586)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (824586)------------------------------
% 0.21/0.28 % (824586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (824586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (824586)CaDiCaL version: 2.1.3
% 0.21/0.28 % (824586)Termination reason: Refutation
% 0.21/0.28 % (824586)Time elapsed: 0.002 s
% 0.21/0.28 % (824586)Peak memory usage: 12 MB
% 0.21/0.28 % (824586)Instructions burned: 3 (million)
% 0.21/0.28 % (824571)Success in time 0.036 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------