%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO103^5 : 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 : n007.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 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 55 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 435 ( 44 ~; 28 |; 28 &; 335 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 ^; 88 !; 6 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
imp: $i > $i > $i ).
thf(func_def_1,type,
cT: $i > $o ).
thf(func_def_2,type,
nt: $i > $i ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X2: $i,X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM147) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X2: $i,X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i,X1: $i] : ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) )
& ! [X2: $i,X3: $i,X4: $i] : ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X3 @ X2 ) ) @ ( imp @ ( imp @ X4 @ X3 ) @ ( imp @ X4 @ X2 ) ) ) )
& ! [X5: $i,X6: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X6 ) @ ( nt @ X5 ) ) @ ( imp @ X5 @ X6 ) ) )
& ! [X7: $i,X8: $i] :
( ~ ( cT @ X8 )
| ( cT @ X7 )
| ~ ( cT @ ( imp @ X8 @ X7 ) ) )
& ? [X9: $i] :
~ ( cT @ ( imp @ X9 @ X9 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) ) )
& ! [X4: $i,X3: $i,X2: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X3 @ X2 ) ) @ ( imp @ ( imp @ X4 @ X3 ) @ ( imp @ X4 @ X2 ) ) ) ) )
& ! [X5: $i,X6: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X6 ) @ ( nt @ X5 ) ) @ ( imp @ X5 @ X6 ) ) ) )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cT @ X8 ) )
| ( $true
= ( cT @ X7 ) )
| ( $true
!= ( cT @ ( imp @ X8 @ X7 ) ) ) )
& ? [X9: $i] :
( $true
!= ( cT @ ( imp @ X9 @ X9 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X5: $i,X6: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X6 ) @ ( nt @ X5 ) ) @ ( imp @ X5 @ X6 ) ) ) )
& ? [X9: $i] :
( $true
!= ( cT @ ( imp @ X9 @ X9 ) ) )
& ! [X4: $i,X3: $i,X2: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X3 @ X2 ) ) @ ( imp @ ( imp @ X4 @ X3 ) @ ( imp @ X4 @ X2 ) ) ) ) )
& ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ X1 @ ( imp @ X0 @ X1 ) ) ) )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cT @ X8 ) )
| ( $true
!= ( cT @ ( imp @ X8 @ X7 ) ) )
| ( $true
= ( cT @ X7 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ? [X2: $i] :
( $true
!= ( cT @ ( imp @ X2 @ X2 ) ) )
& ! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) ) )
& ! [X6: $i,X7: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X6 @ X7 ) ) ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cT @ X9 ) )
| ( $true
!= ( cT @ ( imp @ X9 @ X8 ) ) )
| ( $true
= ( cT @ X8 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ( $true
!= ( cT @ ( imp @ sK0 @ sK0 ) ) )
& ! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) ) )
& ! [X6: $i,X7: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X6 @ X7 ) ) ) )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cT @ X9 ) )
| ( $true
!= ( cT @ ( imp @ X9 @ X8 ) ) )
| ( $true
= ( cT @ X8 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f6]) ).
thf(f8,plain,
! [X8: $i,X9: $i] :
( ( $true
!= ( cT @ ( imp @ X9 @ X8 ) ) )
| ( $true
= ( cT @ X8 ) )
| ( $true
!= ( cT @ X9 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X6: $i,X7: $i] :
( $true
= ( cT @ ( imp @ X7 @ ( imp @ X6 @ X7 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( $true
!= ( cT @ ( imp @ sK0 @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f29,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) )
| ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f8,f10]) ).
thf(f30,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
| ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f37,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) )
| ( $true != $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) ) ),
inference(superposition,[],[f8,f30]) ).
thf(f38,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) )
| ( $true
= ( cT @ ( imp @ X0 @ X2 ) ) )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f38,f9]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f53,plain,
! [X0: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[],[f50,f9]) ).
thf(f63,plain,
! [X0: $i] :
( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f67,plain,
$true != $true,
inference(superposition,[],[f11,f63]) ).
thf(f71,plain,
$false,
inference(trivial_inequality_removal,[],[f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO103^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n007.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:32:02 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.25 % (3595749)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (3595758)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2108432794:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.25 % (3595758) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3595749-3595758"...
% 0.10/0.25 % (3595760)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.25 % (3595760)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.10/0.25 % (3595758)...printing done.
% 0.10/0.25 % (3595758)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (3595758)------------------------------
% 0.10/0.25 % (3595758)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (3595758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (3595758)CaDiCaL version: 2.1.3
% 0.10/0.25 % (3595758)Termination reason: Refutation
% 0.10/0.25 % (3595758)Time elapsed: 0.004 s
% 0.10/0.25 % (3595758)Peak memory usage: 12 MB
% 0.10/0.25 % (3595758)Instructions burned: 10 (million)
% 0.10/0.25 % (3595749)Success in time 0.029 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------