%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV433^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:38:37 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 326 ( 121 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 217 ( 61 ~; 108 |; 6 &; 37 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 62 !; 6 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $i > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finj) ).
thf(f2,conjecture,
! [X1: $i,X2: $i,X0: $i] :
( ( X0 = X1 )
| ( X1 = X2 )
| ( X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less3) ).
thf(f3,negated_conjecture,
~ ! [X1: $i,X2: $i,X0: $i] :
( ( X0 = X1 )
| ( X1 = X2 )
| ( X0 = X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f5,plain,
? [X1: $i,X2: $i,X0: $i] :
( ( X0 != X1 )
& ( X1 != X2 )
& ( X0 != X2 ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f6,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( X0 != X1 )
& ( X1 != X2 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( sK0 != sK2 )
& ( sK0 != sK1 )
& ( sK2 != sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
sK2 != sK1,
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( f @ X0 )
!= ( f @ X1 ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( ( f @ X1 )
= $true )
| ( X0 = X1 )
| ( ( f @ X0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f15,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( f @ X0 )
= $false )
| ( ( f @ X1 )
= $false ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( f @ X2 )
= $false )
| ( X0 = X1 )
| ( X0 = X2 )
| ( $false = $true )
| ( ( f @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f14,f15]) ).
thf(f28,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( f @ X2 )
= $false )
| ( X0 = X2 )
| ( ( f @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( f @ X3 )
= $true )
| ( ( f @ X1 )
= $true )
| ( X0 = X1 )
| ( X2 = X3 )
| ( $false = $true )
| ( X0 = X2 ) ),
inference(constrained_superposition,[],[f14,f28]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ( ( f @ X1 )
= $true )
| ( ( f @ X3 )
= $true )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f142,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X1 )
| ( sK2 = X2 )
| ( ( f @ X1 )
= $true )
| ( sK1 != X0 )
| ( ( f @ X2 )
= $true ) ),
inference(constrained_superposition,[],[f8,f51]) ).
thf(f203,definition,
( spl3_1
<=> ! [X2: $i,X0: $i] :
( ( sK1 != X0 )
| ( ( f @ X2 )
= $true )
| ( X0 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f204,plain,
( ! [X2: $i,X0: $i] :
( ( sK1 != X0 )
| ( X0 = X2 )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,definition,
( spl3_2
<=> ! [X1: $i] :
( ( sK2 = X1 )
| ( ( f @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f207,plain,
( ! [X1: $i] :
( ( ( f @ X1 )
= $true )
| ( sK2 = X1 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f219,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f142,f206,f203]) ).
thf(f226,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( f @ X1 )
= $false )
| ( X0 = X1 )
| ( sK2 = X0 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f15,f207]) ).
thf(f233,plain,
( ! [X0: $i,X1: $i] :
( ( sK2 = X0 )
| ( ( f @ X1 )
= $false )
| ( X0 = X1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f271,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $false = $true )
| ( sK2 = X1 )
| ( sK2 = X0 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f233,f207]) ).
thf(f302,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( sK2 = X0 )
| ( sK2 = X1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f309,definition,
( spl3_5
<=> ( ( f @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f310,plain,
( ( ( f @ sK2 )
!= $false )
| spl3_5 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f311,plain,
( ( ( f @ sK2 )
= $false )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f338,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $true )
| ( $false = $true )
| ( sK2 = X0 ) )
| ~ spl3_5 ),
inference(constrained_superposition,[],[f311,f14]) ).
thf(f362,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $true )
| ( sK2 = X0 ) )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f387,plain,
( ! [X0: $i,X1: $i] :
( ( sK1 != X0 )
| ( sK2 = X1 )
| ( X0 = X1 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f8,f302]) ).
thf(f407,plain,
( ! [X0: $i] :
( ( sK2 = X0 )
| ( sK1 = X0 ) )
| ~ spl3_2 ),
inference(equality_resolution,[],[f387]) ).
thf(f413,definition,
( spl3_9
<=> ! [X4: $i] :
( ( ( f @ X4 )
= $true )
| ( sK1 = X4 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
thf(f414,plain,
( ! [X4: $i] :
( ( ( f @ X4 )
= $true )
| ( sK1 = X4 ) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f413]) ).
thf(f417,plain,
( spl3_2
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f362,f309,f206]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( sK0 != X0 )
| ( sK1 = X0 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f10,f407]) ).
thf(f431,plain,
( ( sK0 = sK1 )
| ( sK0 != sK0 )
| ~ spl3_2 ),
inference(imitation,[],[f428]) ).
thf(f435,plain,
( ( sK0 = sK1 )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f442,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f435,f9]) ).
thf(f443,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f442]) ).
thf(f450,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $false )
| ( $false != $false )
| ( sK2 = X0 ) )
| spl3_5 ),
inference(constrained_superposition,[],[f310,f15]) ).
thf(f463,plain,
( ! [X0: $i] :
( ( ( f @ X0 )
= $false )
| ( sK2 = X0 ) )
| spl3_5 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f592,plain,
( ! [X2: $i] :
( ( sK1 = X2 )
| ( sK1 != sK1 )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_1 ),
inference(imitation,[],[f204]) ).
thf(f596,plain,
( ! [X2: $i] :
( ( sK1 = X2 )
| ( ( f @ X2 )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f598,plain,
( spl3_9
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f596,f203,f413]) ).
thf(f607,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( sK1 = X0 )
| ( sK2 = X0 ) )
| spl3_5
| ~ spl3_9 ),
inference(constrained_superposition,[],[f414,f463]) ).
thf(f619,plain,
( ! [X0: $i] :
( ( sK2 = X0 )
| ( sK1 = X0 ) )
| spl3_5
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f633,plain,
( ! [X0: $i] :
( ( sK0 != X0 )
| ( sK1 = X0 ) )
| spl3_5
| ~ spl3_9 ),
inference(constrained_superposition,[],[f10,f619]) ).
thf(f636,plain,
( ( sK0 != sK0 )
| ( sK0 = sK1 )
| spl3_5
| ~ spl3_9 ),
inference(imitation,[],[f633]) ).
thf(f640,plain,
( ( sK0 = sK1 )
| spl3_5
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f636]) ).
thf(f643,plain,
( $false
| spl3_5
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f640,f9]) ).
thf(f644,plain,
( spl3_5
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f643]) ).
cnf(s5,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f219]) ).
cnf(s17,plain,
( spl3_2
| ~ spl3_5 ),
inference(sat_conversion,[],[f417]) ).
cnf(s25,plain,
~ spl3_2,
inference(sat_conversion,[],[f443]) ).
cnf(s43,plain,
( ~ spl3_1
| spl3_9 ),
inference(sat_conversion,[],[f598]) ).
cnf(s50,plain,
( spl3_5
| ~ spl3_9 ),
inference(sat_conversion,[],[f644]) ).
cnf(s59,plain,
~ spl3_5,
inference(rat,[],[s17,s25]) ).
cnf(s60,plain,
~ spl3_9,
inference(rat,[],[s50,s59]) ).
cnf(s62,plain,
~ spl3_1,
inference(rat,[],[s43,s60]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s5,s25,s62]) ).
thf(f652,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV433^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n001.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 15:52:51 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 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
% 0.20/0.29 % (1408125)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1408132)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1638904036:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (1408132)Refutation not found, incomplete strategy
% 0.20/0.29 % (1408132)------------------------------
% 0.20/0.29 % (1408132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1408132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1408132)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1408132)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1408132)Time elapsed: 0.001 s
% 0.20/0.29 % (1408132)Peak memory usage: 12 MB
% 0.20/0.29 % (1408132)------------------------------
% 0.20/0.29 % (1408132)------------------------------
% 0.20/0.29 % (1408130)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2097661124:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (1408131)lrs+10_16_si=on:nwc=1.5:random_seed=1959867509:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (1408134)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1650922581:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (1408133)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=524738961: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)
% 0.20/0.29 % (1408135)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3620259980:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (1408136)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1408136)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.29 % (1408131)Instruction limit reached!
% 0.20/0.29 % (1408131)------------------------------
% 0.20/0.29 % (1408131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1408131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1408131)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1408131)Termination reason: Instruction limit
% 0.20/0.29 % (1408131)Termination phase: Saturation
% 0.20/0.29 % (1408131)Time elapsed: 0.010 s
% 0.20/0.29 % (1408131)Peak memory usage: 12 MB
% 0.20/0.29 % (1408131)Instructions burned: 18 (million)
% 0.20/0.29 % (1408134)Instruction limit reached!
% 0.20/0.29 % (1408134)------------------------------
% 0.20/0.29 % (1408134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1408134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1408134)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1408134)Termination reason: Instruction limit
% 0.20/0.29 % (1408134)Termination phase: Saturation
% 0.20/0.29 % (1408134)Time elapsed: 0.013 s
% 0.20/0.29 % (1408134)Peak memory usage: 12 MB
% 0.20/0.29 % (1408134)Instructions burned: 26 (million)
% 0.20/0.29 % (1408136)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2144949403:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (1408130) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1408125-1408130"...
% 0.20/0.29 % (1408138)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1114524418:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (1408130)...printing done.
% 0.20/0.29 % (1408130)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1408130)------------------------------
% 0.20/0.29 % (1408130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1408130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1408130)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1408130)Termination reason: Refutation
% 0.20/0.29 % (1408130)Time elapsed: 0.024 s
% 0.20/0.29 % (1408130)Peak memory usage: 13 MB
% 0.20/0.29 % (1408130)Instructions burned: 44 (million)
% 0.20/0.29 % (1408125)Success in time 0.058 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------