%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO504^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:48:09 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 15 unt; 0 typ; 8 def)
% Number of atoms : 507 ( 96 equ; 0 cnn)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 321 ( 67 ~; 64 |; 42 &; 130 @)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $o ).
thf(func_def_1,type,
b: $o ).
thf(func_def_2,type,
h: $o > $o > $o ).
thf(func_def_3,type,
i: $o > $o > $o ).
thf(func_def_4,type,
g: ( $o > $o > $o ) > $o ).
thf(func_def_5,type,
f: ( ( $o > $o > $o ) > $o ) > $o ).
thf(f1,conjecture,
( ( ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b )
& ( b
| ( a
= ( i @ a @ b ) ) )
& a
& ( b
= ( h @ a @ b ) ) )
=> ( f @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',claim) ).
thf(f2,negated_conjecture,
~ ( ( ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b )
& ( b
| ( a
= ( i @ a @ b ) ) )
& a
& ( b
= ( h @ a @ b ) ) )
=> ( f @ g ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b )
& ( b
| ( a
= ( i @ a @ b ) ) )
& a
& ( b
= ( h @ a @ b ) ) )
=> ( f @ g ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ( ( h @ a @ b )
= $true )
<=> ( ( a = $true )
& ( b = $true ) ) )
& ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) )
& ( ( h @ a @ b )
= $true )
& ( ( i @ a @ b )
= ( f @ g ) ) )
=> ( ( f @ g )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( f @ g )
!= $true )
& ( ( ( h @ a @ b )
= $true )
<=> ( ( a = $true )
& ( b = $true ) ) )
& ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) )
& ( ( h @ a @ b )
= $true )
& ( ( i @ a @ b )
= ( f @ g ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( f @ g )
!= $true )
& ( ( i @ a @ b )
= ( f @ g ) )
& ( ( h @ a @ b )
= $true )
& ( ( ( h @ a @ b )
= $true )
<=> ( ( a = $true )
& ( b = $true ) ) )
& ( ( ( b = $true )
| ( a = $true ) )
<=> ( ( i @ a @ b )
= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( ( f @ g )
!= $true )
& ( ( i @ a @ b )
= ( f @ g ) )
& ( ( h @ a @ b )
= $true )
& ( ( ( h @ a @ b )
= $true )
| ( a != $true )
| ( b != $true ) )
& ( ( ( a = $true )
& ( b = $true ) )
| ( ( h @ a @ b )
!= $true ) )
& ( ( b = $true )
| ( a = $true )
| ( ( i @ a @ b )
!= $true ) )
& ( ( ( i @ a @ b )
= $true )
| ( ( b != $true )
& ( a != $true ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ( f @ g )
!= $true )
& ( ( i @ a @ b )
= ( f @ g ) )
& ( ( h @ a @ b )
= $true )
& ( ( ( h @ a @ b )
= $true )
| ( a != $true )
| ( b != $true ) )
& ( ( ( a = $true )
& ( b = $true ) )
| ( ( h @ a @ b )
!= $true ) )
& ( ( b = $true )
| ( a = $true )
| ( ( i @ a @ b )
!= $true ) )
& ( ( ( i @ a @ b )
= $true )
| ( ( b != $true )
& ( a != $true ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
( ( ( i @ a @ b )
= $true )
| ( a != $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( ( h @ a @ b )
!= $true )
| ( b = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( ( h @ a @ b )
!= $true )
| ( a = $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( h @ a @ b )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( i @ a @ b )
= ( f @ g ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( ( f @ g )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f20,plain,
( ( ( i @ a @ b )
= $false )
| ( ( f @ g )
= $true ) ),
inference(iff_proxy_clausification,[],[f16]) ).
thf(f22,definition,
( spl0_1
<=> ( ( i @ a @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f24,plain,
( ( ( i @ a @ b )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f26,definition,
( spl0_2
<=> ( b = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f27,plain,
( ( b = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f31,definition,
( spl0_3
<=> ( a = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f32,plain,
( ( a = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl0_4
<=> ( ( h @ a @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f39,plain,
spl0_4,
inference(avatar_split_clause,[],[f15,f35]) ).
thf(f40,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f12,f35,f26]) ).
thf(f42,definition,
( spl0_5
<=> ( ( f @ g )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f46,definition,
( spl0_6
<=> ( ( i @ a @ b )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f48,plain,
( ( ( i @ a @ b )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f46,f42]) ).
thf(f56,plain,
( ~ spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f9,f22,f31]) ).
thf(f57,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f17,f42]) ).
thf(f58,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f13,f35,f31]) ).
thf(f61,plain,
( ( $true
= ( i @ $true @ b ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f24,f32]) ).
thf(f62,plain,
( ( $true
= ( i @ $true @ $true ) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f61,f27]) ).
thf(f64,definition,
( spl0_8
<=> ( $true
= ( i @ $true @ $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f66,plain,
( ( $true
= ( i @ $true @ $true ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f67,plain,
( spl0_8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f62,f31,f26,f22,f64]) ).
thf(f75,plain,
( ( $false
= ( i @ $true @ b ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f48,f32]) ).
thf(f76,plain,
( ( $false
= ( i @ $true @ $true ) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f75,f27]) ).
thf(f78,definition,
( spl0_10
<=> ( $false
= ( i @ $true @ $true ) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f80,plain,
( ( $false
= ( i @ $true @ $true ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f81,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f76,f46,f31,f26,f78]) ).
thf(f82,plain,
( ( $false = $true )
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f80,f66]) ).
thf(f84,plain,
( $false
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f85,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f84]) ).
cnf(s3,plain,
spl0_4,
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s8,plain,
( spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s9,plain,
~ spl0_5,
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f58]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f67]) ).
cnf(s13,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f81]) ).
cnf(s14,plain,
( ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f85]) ).
cnf(s16,plain,
spl0_6,
inference(rat,[],[s5,s9]) ).
cnf(s17,plain,
spl0_3,
inference(rat,[],[s10,s3]) ).
cnf(s18,plain,
spl0_2,
inference(rat,[],[s4,s3]) ).
cnf(s19,plain,
spl0_1,
inference(rat,[],[s8,s17]) ).
cnf(s20,plain,
spl0_10,
inference(rat,[],[s13,s17,s16,s18]) ).
cnf(s22,plain,
spl0_8,
inference(rat,[],[s11,s18,s17,s19]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s14,s20,s22]) ).
thf(f88,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO504^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n011.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 17:11:31 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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
% 0.22/0.29 % (376484)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (376501)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3985062239:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.29 % (376501) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-376484-376501"...
% 0.22/0.29 % (376501)...printing done.
% 0.22/0.29 % (376501)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (376501)------------------------------
% 0.22/0.29 % (376501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (376501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (376501)CaDiCaL version: 2.1.3
% 0.22/0.29 % (376501)Termination reason: Refutation
% 0.22/0.29 % (376501)Time elapsed: 0.002 s
% 0.22/0.29 % (376501)Peak memory usage: 13 MB
% 0.22/0.29 % (376501)Instructions burned: 4 (million)
% 0.22/0.29 % (376484)Success in time 0.032 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------