%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU852^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:34:17 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 418 ( 147 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 463 ( 102 ~; 102 |; 47 &; 175 @)
% ( 10 <=>; 25 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 68 !; 21 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(func_def_6,type,
sK3: a ).
thf(func_def_7,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM36_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
<=> ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X2 @ X3 )
& ( X0 @ X3 ) )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X2 @ X4 ) ) )
=> ( ! [X5: a] :
( ( X0 @ X5 )
=> ( X1 @ X5 ) )
<=> ! [X6: a] :
( ( ~ ( X1 @ X6 )
& ( X2 @ X6 )
& ( X0 @ X6 ) )
=> ( X1 @ X6 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ( ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( ( X1 @ X5 )
= $true ) )
<=> ! [X6: a] :
( ( ( ( X1 @ X6 )
!= $true )
& ( ( X2 @ X6 )
= $true )
& ( ( X0 @ X6 )
= $true ) )
=> ( ( X1 @ X6 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ( ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( ( X1 @ X5 )
= $true ) )
<=> ! [X6: a] :
( ( ( ( X1 @ X6 )
!= $true )
& ( ( X2 @ X6 )
= $true )
& ( ( X0 @ X6 )
= $true ) )
=> ( ( X1 @ X6 )
= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) )
<~> ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
| ( ( X1 @ X6 )
= $true )
| ( ( X2 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) )
<~> ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
| ( ( X1 @ X6 )
= $true )
| ( ( X2 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X6: a] :
( ( ( X1 @ X6 )
!= $true )
& ( ( X1 @ X6 )
!= $true )
& ( ( X2 @ X6 )
= $true )
& ( ( X0 @ X6 )
= $true ) )
| ? [X5: a] :
( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) )
& ( ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
| ( ( X1 @ X6 )
= $true )
| ( ( X2 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true ) )
| ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X6: a] :
( ( ( X1 @ X6 )
!= $true )
& ( ( X1 @ X6 )
!= $true )
& ( ( X2 @ X6 )
= $true )
& ( ( X0 @ X6 )
= $true ) )
| ? [X5: a] :
( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) )
& ( ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
| ( ( X1 @ X6 )
= $true )
| ( ( X2 @ X6 )
!= $true )
| ( ( X0 @ X6 )
!= $true ) )
| ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ? [X3: a] :
( ( ( X1 @ X3 )
!= $true )
& ( ( X1 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true )
& ( ( X0 @ X3 )
= $true ) )
| ? [X4: a] :
( ( $true
!= ( X1 @ X4 ) )
& ( ( X0 @ X4 )
= $true ) ) )
& ( ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( ( X1 @ X5 )
= $true )
| ( $true
!= ( X2 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) )
| ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
| ( ( X0 @ X6 )
!= $true ) ) )
& ! [X7: a] :
( ( $true
= ( X2 @ X7 ) )
| ( $true
!= ( X1 @ X7 ) ) )
& ! [X8: a] :
( ( $true
= ( X2 @ X8 ) )
| ( $true
!= ( X0 @ X8 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( ( $true
!= ( sK1 @ sK3 ) )
& ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK2 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) ) )
| ( ( $true
!= ( sK1 @ sK4 ) )
& ( $true
= ( sK0 @ sK4 ) ) ) )
& ( ! [X5: a] :
( ( $true
= ( sK1 @ X5 ) )
| ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) )
| ! [X6: a] :
( ( $true
= ( sK1 @ X6 ) )
| ( $true
!= ( sK0 @ X6 ) ) ) )
& ! [X7: a] :
( ( $true
= ( sK2 @ X7 ) )
| ( $true
!= ( sK1 @ X7 ) ) )
& ! [X8: a] :
( ( $true
= ( sK2 @ X8 ) )
| ( $true
!= ( sK0 @ X8 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f10]) ).
thf(f12,plain,
! [X8: a] :
( ( $true
= ( sK2 @ X8 ) )
| ( $true
!= ( sK0 @ X8 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
! [X6: a,X5: a] :
( ( $true
= ( sK1 @ X5 ) )
| ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( sK1 @ X6 ) )
| ( $true
!= ( sK0 @ X6 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f21,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f22,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ( $true
!= ( sK1 @ sK4 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f25,plain,
! [X6: a,X5: a] :
( ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK2 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( sK1 @ X6 ) )
| ( $true
!= ( sK0 @ X6 ) ) ),
inference(duplicate_literal_removal,[],[f14]) ).
thf(f26,plain,
! [X6: a,X5: a] :
( ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( sK1 @ X6 ) )
| ( $true
!= ( sK0 @ X6 ) ) ),
inference(forward_subsumption_resolution,[],[f25,f12]) ).
thf(f28,definition,
( spl5_1
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f30,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f32,definition,
( spl5_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f15,f32,f28]) ).
thf(f37,definition,
( spl5_3
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f39,plain,
( ( $true
!= ( sK1 @ sK4 ) )
| spl5_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( ~ spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f16,f32,f37]) ).
thf(f48,definition,
( spl5_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f50,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| spl5_5 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f53,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f21,f48,f28]) ).
thf(f54,plain,
( ~ spl5_3
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f22,f48,f37]) ).
thf(f56,definition,
( spl5_6
<=> ! [X6: a] :
( ( $true
= ( sK1 @ X6 ) )
| ( $true
!= ( sK0 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f57,plain,
( ! [X6: a] :
( ( $true
!= ( sK0 @ X6 ) )
| ( $true
= ( sK1 @ X6 ) ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f58,plain,
( spl5_6
| spl5_6 ),
inference(avatar_split_clause,[],[f26,f56,f56]) ).
thf(f59,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK3 ) )
| ~ spl5_2
| ~ spl5_6 ),
inference(constrained_superposition,[],[f57,f34]) ).
thf(f60,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl5_2
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( $false
| ~ spl5_2
| spl5_5
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f60,f50]) ).
thf(f62,plain,
( ~ spl5_2
| spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f61]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK4 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(constrained_superposition,[],[f57,f30]) ).
thf(f64,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl5_1
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f65,plain,
( $false
| ~ spl5_1
| spl5_3
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f64,f39]) ).
thf(f66,plain,
( ~ spl5_1
| spl5_3
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f65]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
( spl5_2
| ~ spl5_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s7,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f53]) ).
cnf(s8,plain,
( ~ spl5_3
| ~ spl5_5 ),
inference(sat_conversion,[],[f54]) ).
cnf(s9,plain,
( spl5_6
| spl5_6 ),
inference(sat_conversion,[],[f58]) ).
cnf(s10,plain,
spl5_6,
inference(rat,[],[s9]) ).
cnf(s11,plain,
( ~ spl5_2
| spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f62]) ).
cnf(s12,plain,
( ~ spl5_1
| spl5_3
| ~ spl5_6 ),
inference(sat_conversion,[],[f66]) ).
cnf(s13,plain,
spl5_1,
inference(rat,[],[s11,s1,s7,s10]) ).
cnf(s14,plain,
spl5_3,
inference(rat,[],[s12,s10,s13]) ).
cnf(s15,plain,
~ spl5_5,
inference(rat,[],[s8,s14]) ).
cnf(s17,plain,
spl5_2,
inference(rat,[],[s2,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s11,s10,s15,s17]) ).
thf(f67,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU852^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n016.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 14:44:49 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (440374)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (440383)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3895142918:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (440383)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (440380)% WARNING: option uhcvi not known.
% 0.21/0.28 % (440383) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-440374-440383"...
% 0.21/0.28 % (440383)...printing done.
% 0.21/0.28 % (440383)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (440383)------------------------------
% 0.21/0.28 % (440383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (440383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (440383)CaDiCaL version: 2.1.3
% 0.21/0.28 % (440383)Termination reason: Refutation
% 0.21/0.28 % (440383)Time elapsed: 0.002 s
% 0.21/0.28 % (440383)Peak memory usage: 12 MB
% 0.21/0.28 % (440383)Instructions burned: 4 (million)
% 0.21/0.28 % (440374)Success in time 0.041 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------