%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV416^5 : 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 : n013.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 08:38:36 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 1
% Syntax : Number of formulae : 65 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 873 ( 233 equ; 0 cnn)
% Maximal formula atoms : 11 ( 13 avg)
% Number of connectives : 519 ( 117 ~; 146 |; 24 &; 200 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 21 !; 9 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $o ).
thf(func_def_1,type,
cB: $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(f1,conjecture,
( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDUAL_EG3_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
& ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> cG ) )
=> ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> cG )
| ( ( ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) )
& ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) ) )
=> cG ) )
=> ( ! [X3: $i] :
( ( cA @ X3 )
=> ( cB @ X3 ) )
=> cG ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ( cG = $true ) )
| ( ( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
=> ( $true
= ( cB @ X2 ) ) )
& ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( cB @ X1 ) ) ) )
=> ( cG = $true ) ) )
=> ( ! [X3: $i] :
( ( $true
= ( cA @ X3 ) )
=> ( $true
= ( cB @ X3 ) ) )
=> ( cG = $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cG != $true )
& ! [X3: $i] :
( ( $true
!= ( cA @ X3 ) )
| ( $true
= ( cB @ X3 ) ) )
& ( ( cG = $true )
| ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( ( cA @ X2 )
= $true ) )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( cG = $true )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) )
| ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( ( cA @ X2 )
= $true ) ) )
& ! [X3: $i] :
( ( $true
!= ( cA @ X3 ) )
| ( $true
= ( cB @ X3 ) ) )
& ( cG != $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( cG = $true )
| ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ( ( cB @ X0 )
!= $true ) )
| ? [X1: $i] :
( ( $true
= ( cA @ X1 ) )
& ( $true
!= ( cB @ X1 ) ) )
| ( cG = $true )
| ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( ( cA @ X2 )
= $true ) ) )
& ! [X3: $i] :
( ( $true
!= ( cA @ X3 ) )
| ( $true
= ( cB @ X3 ) ) )
& ( cG != $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cG = $true )
| ( ( $true
= ( cA @ sK0 ) )
& ( $true
!= ( cB @ sK0 ) ) )
| ( ( ( cA @ sK1 )
= $true )
& ( ( cB @ sK1 )
!= $true ) )
| ( cG = $true )
| ( ( $true
!= ( cB @ sK2 ) )
& ( $true
= ( cA @ sK2 ) ) ) )
& ! [X3: $i] :
( ( $true
!= ( cA @ X3 ) )
| ( $true
= ( cB @ X3 ) ) )
& ( cG != $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
cG != $true,
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X3: $i] :
( ( $true
= ( cB @ X3 ) )
| ( $true
!= ( cA @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( cG = $true )
| ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( ( cB @ sK1 )
!= $true )
| ( $true
= ( cA @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK0 ) )
| ( ( cB @ sK1 )
!= $true )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( cG = $true )
| ( cG = $true )
| ( ( cA @ sK1 )
= $true )
| ( $true
= ( cA @ sK2 ) )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( cG = $true )
| ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK0 ) )
| ( ( cB @ sK1 )
!= $true )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( $true
= ( cA @ sK0 ) )
| ( cG = $true )
| ( ( cA @ sK1 )
= $true )
| ( $true
= ( cA @ sK2 ) )
| ( cG = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( ( ( cA @ sK1 )
= $true )
| ( cG = $true )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( ( cG = $true )
| ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f12]) ).
thf(f21,plain,
( ( ( cB @ sK1 )
!= $true )
| ( cG = $true )
| ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f15]) ).
thf(f22,plain,
( ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f18]) ).
thf(f23,plain,
( ( ( cA @ sK1 )
= $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f17]) ).
thf(f24,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f11]) ).
thf(f25,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cB @ sK0 ) )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f14]) ).
thf(f26,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( ( cA @ sK1 )
= $true )
| ( cG = $true ) ),
inference(duplicate_literal_removal,[],[f13]) ).
thf(f27,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( ( cB @ sK1 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f16]) ).
thf(f31,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(forward_subsumption_resolution,[],[f20,f9]) ).
thf(f32,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true
!= ( cB @ sK2 ) )
| ( $true != $true )
| ( ( cA @ sK1 )
!= $true ) ),
inference(superposition,[],[f31,f10]) ).
thf(f33,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f21,f9]) ).
thf(f35,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( $true != $true )
| ( ( cA @ sK1 )
!= $true ) ),
inference(superposition,[],[f34,f10]) ).
thf(f36,plain,
( ( ( cA @ sK1 )
!= $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cA @ sK2 ) )
| ( $true
!= ( cB @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f33,f10]) ).
thf(f38,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f41,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( $true
= ( cA @ sK0 ) )
| ( ( cA @ sK1 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f22,f9]) ).
thf(f42,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true != $true )
| ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(superposition,[],[f41,f10]) ).
thf(f43,plain,
( ( ( cA @ sK1 )
= $true )
| ( $true
!= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f48,plain,
( ( ( cA @ sK1 )
= $true )
| ( cG = $true )
| ( $true
= ( cA @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f23,f43]) ).
thf(f49,plain,
( ( ( cA @ sK1 )
= $true )
| ( $true
= ( cA @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f48,f9]) ).
thf(f51,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[],[f36,f49]) ).
thf(f52,plain,
( ( $true != $true )
| ( $true
= ( cA @ sK0 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( cA @ sK2 ) )
| ( $true
= ( cA @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(forward_subsumption_resolution,[],[f24,f9]) ).
thf(f55,plain,
( ( ( cA @ sK1 )
!= $true )
| ( $true != $true )
| ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK2 ) ) ),
inference(superposition,[],[f54,f10]) ).
thf(f56,plain,
( ( $true
= ( cA @ sK2 ) )
| ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f57,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( ( cA @ sK1 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f56,f38]) ).
thf(f60,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( cG = $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f25,f33]) ).
thf(f61,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f60,f9]) ).
thf(f62,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(superposition,[],[f61,f10]) ).
thf(f63,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f69,plain,
( ( $true
!= ( cB @ sK0 ) )
| ( $true
= ( cA @ sK2 ) )
| ( cG = $true ) ),
inference(forward_subsumption_resolution,[],[f26,f57]) ).
thf(f70,plain,
( ( cG = $true )
| ( $true
!= ( cB @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f69,f63]) ).
thf(f71,plain,
( $true
!= ( cB @ sK0 ) ),
inference(forward_subsumption_resolution,[],[f70,f9]) ).
thf(f72,plain,
( ( $true
!= ( cA @ sK0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f71,f10]) ).
thf(f73,plain,
( $true
!= ( cA @ sK0 ) ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f74,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) )
| ( cG = $true ) ),
inference(forward_subsumption_resolution,[],[f27,f73]) ).
thf(f75,plain,
( ( ( cB @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(forward_subsumption_resolution,[],[f74,f9]) ).
thf(f76,plain,
( ( $true != $true )
| ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cB @ sK2 ) ) ),
inference(superposition,[],[f75,f10]) ).
thf(f77,plain,
( ( $true
!= ( cB @ sK2 ) )
| ( ( cA @ sK1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f78,plain,
( ( $true != $true )
| ( $true
!= ( cA @ sK2 ) )
| ( ( cA @ sK1 )
!= $true ) ),
inference(superposition,[],[f77,f10]) ).
thf(f79,plain,
( ( ( cA @ sK1 )
!= $true )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cA @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[],[f79,f49]) ).
thf(f84,plain,
( ( $true
= ( cA @ sK0 ) )
| ( $true
!= ( cA @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f86,plain,
( $true
= ( cA @ sK0 ) ),
inference(forward_subsumption_resolution,[],[f84,f53]) ).
thf(f87,plain,
$false,
inference(forward_subsumption_resolution,[],[f86,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV416^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 15:45:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.07/0.26 % (2276411)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (2276420)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3805849988:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.07/0.26 % (2276420) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2276411-2276420"...
% 0.07/0.26 % (2276420)...printing done.
% 0.07/0.26 % (2276420)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.26 % (2276420)------------------------------
% 0.20/0.26 % (2276420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (2276420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (2276420)CaDiCaL version: 2.1.3
% 0.20/0.26 % (2276420)Termination reason: Refutation
% 0.20/0.26 % (2276420)Time elapsed: 0.002 s
% 0.20/0.26 % (2276420)Peak memory usage: 12 MB
% 0.20/0.26 % (2276420)Instructions burned: 7 (million)
% 0.20/0.26 % (2276411)Success in time 0.028 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------