%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO375^5 : 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 : n005.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 08:47:33 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 178 ( 36 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 161 ( 50 ~; 42 |; 3 &; 52 @)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 22 !; 6 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sK0: $i > $o ).
thf(func_def_2,type,
sK1: $i > $o ).
thf(f1,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X0 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_SET1) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X0 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
<=> ( X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
= ( X1 @ X3 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: $i > $o,X0: $i > $o] :
( ? [X3: $i] :
( ( X0 @ X3 )
!= ( X1 @ X3 ) )
& ! [X2: $i] :
( ( X0 @ X2 )
= ( X1 @ X2 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i > $o,X1: $i > $o] :
( ? [X2: $i] :
( ( X0 @ X2 )
!= ( X1 @ X2 ) )
& ! [X3: $i] :
( ( X0 @ X3 )
= ( X1 @ X3 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) )
& ! [X3: $i] :
( ( sK1 @ X3 )
= ( sK0 @ X3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
! [X3: $i] :
( ( sK1 @ X3 )
= ( sK0 @ X3 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK0 @ sK2 )
!= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X3: $i] :
( ( ( sK0 @ X3 )
= $false )
| ( ( sK1 @ X3 )
= $true ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f13,plain,
! [X3: $i] :
( ( $true
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f8]) ).
thf(f14,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( ( sK0 @ sK2 )
= $true ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f15,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(xor_proxy_clausification,[],[f9]) ).
thf(f17,definition,
( spl3_1
<=> ( ( sK0 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f19,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f21,definition,
( spl3_2
<=> ( ( sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f23,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f15,f21,f17]) ).
thf(f26,definition,
( spl3_3
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f28,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f30,definition,
( spl3_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f14,f30,f26]) ).
thf(f35,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true = $false )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f28,f12]) ).
thf(f37,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f41,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f37,f23]) ).
thf(f42,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f44,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[],[f19,f28]) ).
thf(f45,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f46,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f45]) ).
thf(f48,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f32,f23]) ).
thf(f49,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f49]) ).
thf(f58,plain,
( ( $true = $false )
| ( ( sK1 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f19,f13]) ).
thf(f61,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f68,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_demodulation,[],[f61,f32]) ).
thf(f69,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f70,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f69]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f24]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f43]) ).
cnf(s5,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f46]) ).
cnf(s8,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s11,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s12,plain,
~ spl3_2,
inference(rat,[],[s2,s4,s8]) ).
cnf(s13,plain,
spl3_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
~ spl3_4,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl3_3,
inference(rat,[],[s5,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s14,s15]) ).
thf(f71,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO375^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n005.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:49:16 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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
% 0.21/0.29 % (1908791)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1908796)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3542318615:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1908796) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1908791-1908796"...
% 0.21/0.29 % (1908796)...printing done.
% 0.21/0.29 % (1908796)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1908796)------------------------------
% 0.21/0.30 % (1908796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1908796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1908796)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1908796)Termination reason: Refutation
% 0.21/0.30 % (1908796)Time elapsed: 0.002 s
% 0.21/0.30 % (1908796)Peak memory usage: 13 MB
% 0.21/0.30 % (1908796)Instructions burned: 2 (million)
% 0.21/0.30 % (1908791)Success in time 0.039 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------