%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN356^5 : 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 : n017.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 08:41:40 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 236 ( 49 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 209 ( 22 ~; 15 |; 24 &; 136 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_3,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ( ( cR @ cA @ cB )
& ! [X3: $i,X2: $i] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X2 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X1 )
=> ( ( cQ @ X0 @ X1 )
& ( cR @ X1 @ X0 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLX2107) ).
thf(f2,negated_conjecture,
~ ( ( ( cR @ cA @ cB )
& ! [X3: $i,X2: $i] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X2 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X1 )
=> ( ( cQ @ X0 @ X1 )
& ( cR @ X1 @ X0 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cR @ cA @ cB )
& ! [X0: $i,X1: $i] :
( ( cQ @ X1 @ X0 )
=> ( cQ @ X1 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X3 )
=> ( ( cQ @ X2 @ X3 )
& ( cR @ X3 @ X2 ) ) ) )
=> ( ( cQ @ cA @ cA )
& ( cQ @ cB @ cB ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( $true
= ( cQ @ X1 @ X0 ) )
=> ( $true
= ( cQ @ X1 @ X1 ) ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X3: $i,X2: $i] :
( ( $true
= ( cR @ X2 @ X3 ) )
=> ( ( ( cR @ X3 @ X2 )
= $true )
& ( ( cQ @ X2 @ X3 )
= $true ) ) ) )
=> ( ( ( cQ @ cB @ cB )
= $true )
& ( ( cQ @ cA @ cA )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) )
& ! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ X1 @ X0 ) )
| ( $true
= ( cQ @ X1 @ X1 ) ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cR @ X2 @ X3 ) )
| ( ( ( cR @ X3 @ X2 )
= $true )
& ( ( cQ @ X2 @ X3 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) )
& ! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ X1 @ X0 ) )
| ( $true
= ( cQ @ X1 @ X1 ) ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cR @ X2 @ X3 ) )
| ( ( ( cR @ X3 @ X2 )
= $true )
& ( ( cQ @ X2 @ X3 )
= $true ) ) )
& ( ( cR @ cA @ cB )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( cR @ cA @ cB )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( cR @ X2 @ X3 ) )
| ( ( cQ @ X2 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( cR @ X2 @ X3 ) )
| ( ( cR @ X3 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ X1 @ X0 ) )
| ( $true
= ( cQ @ X1 @ X1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( ( ( cQ @ cA @ cA )
!= $true )
| ( ( cQ @ cB @ cB )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( ( $true != $true )
| ( $true
= ( cQ @ cA @ cB ) ) ),
inference(superposition,[],[f8,f7]) ).
thf(f14,plain,
( $true
= ( cQ @ cA @ cB ) ),
inference(trivial_inequality_removal,[],[f13]) ).
thf(f15,plain,
( ( ( cR @ cB @ cA )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f9,f7]) ).
thf(f16,plain,
( ( cR @ cB @ cA )
= $true ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f18,plain,
( ( $true != $true )
| ( ( cQ @ cB @ cA )
= $true ) ),
inference(superposition,[],[f8,f16]) ).
thf(f20,plain,
( ( cQ @ cB @ cA )
= $true ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f21,plain,
( ( $true != $true )
| ( ( cQ @ cA @ cA )
= $true ) ),
inference(superposition,[],[f10,f14]) ).
thf(f22,plain,
( ( ( cQ @ cB @ cB )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f10,f20]) ).
thf(f23,plain,
( ( cQ @ cB @ cB )
= $true ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( ( cQ @ cA @ cA )
= $true ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f25,plain,
( ( cQ @ cB @ cB )
!= $true ),
inference(forward_subsumption_resolution,[],[f11,f24]) ).
thf(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN356^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.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 16:10:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.23/0.28 % (524398)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (524407)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=636865041:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.28 % (524407) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-524398-524407"...
% 0.23/0.28 % (524407)...printing done.
% 0.23/0.28 % (524407)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 % (524407)------------------------------
% 0.23/0.28 % (524407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (524407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (524407)CaDiCaL version: 2.1.3
% 0.23/0.28 % (524407)Termination reason: Refutation
% 0.23/0.28 % (524407)Time elapsed: 0.001 s
% 0.23/0.28 % (524407)Peak memory usage: 12 MB
% 0.23/0.28 % (524407)Instructions burned: 2 (million)
% 0.23/0.28 % (524398)Success in time 0.034 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------