%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO506^1 : TPTP v9.3.1. Released v4.1.0.
% 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 08:48:09 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 21 unt; 0 typ; 7 def)
% Number of atoms : 193 ( 67 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 186 ( 38 ~; 30 |; 6 &; 109 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 15 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 54 !; 4 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c: $o > $i > $i > $i ).
thf(func_def_4,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
sF2: $i > $i > $i ).
thf(func_def_8,type,
sF3: $i > $i > $i ).
thf(func_def_9,type,
sF4: $o ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( c @ ( X0 = X1 ) @ X0 @ X1 )
= X1 )
| ~ ! [X1: $i,X0: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 )
| ~ ! [X1: $i,X0: $i] :
( X0
= ( c @ $true @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( c @ ( X0 = X1 ) @ X0 @ X1 )
= X1 )
| ~ ! [X1: $i,X0: $i] :
( ( c @ $false @ X0 @ X1 )
= X1 )
| ~ ! [X1: $i,X0: $i] :
( X0
= ( c @ $true @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i] :
( ( c @ ( X0 = X1 ) @ X0 @ X1 )
= X1 )
| ~ ! [X2: $i,X3: $i] :
( ( c @ $false @ X3 @ X2 )
= X2 )
| ~ ! [X4: $i,X5: $i] :
( X5
= ( c @ $true @ X5 @ X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ~ ! [X5: $i,X4: $i] :
( ( c @ $true @ X5 @ X4 )
= X5 )
| ! [X1: $i,X0: $i] :
( ( c @ ( X0 = X1 ) @ X0 @ X1 )
= X1 )
| ~ ! [X3: $i,X2: $i] :
( ( c @ $false @ X3 @ X2 )
= X2 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X5: $i,X4: $i] :
( ( c @ $true @ X5 @ X4 )
= X5 )
& ! [X3: $i,X2: $i] :
( ( c @ $false @ X3 @ X2 )
= X2 )
& ? [X1: $i,X0: $i] :
( ( c @ ( X0 = X1 ) @ X0 @ X1 )
!= X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( ( c @ $true @ X0 @ X1 )
= X0 )
& ! [X2: $i,X3: $i] :
( ( c @ $false @ X2 @ X3 )
= X3 )
& ? [X4: $i,X5: $i] :
( ( c @ ( X5 = X4 ) @ X5 @ X4 )
!= X4 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( ( c @ $true @ X0 @ X1 )
= X0 )
& ! [X2: $i,X3: $i] :
( ( c @ $false @ X2 @ X3 )
= X3 )
& ( sK0
!= ( c @ ( sK1 = sK0 ) @ sK1 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0),skolemize(X5,sK1)],[f6]) ).
thf(f8,plain,
( sK0
!= ( c @ ( sK1 = sK0 ) @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i,X3: $i] :
( ( c @ $false @ X2 @ X3 )
= X3 ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( c @ $true @ X0 @ X1 )
= X0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
! [X0: $i,X1: $i] :
( ( sF2 @ X1 @ X0 )
= ( c @ $true @ X0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f14,plain,
! [X0: $i,X1: $i] :
( ( sF2 @ X1 @ X0 )
= X0 ),
inference(definition_folding,[],[f10,f13]) ).
thf(f15,definition,
! [X2: $i,X3: $i] :
( ( sF3 @ X3 @ X2 )
= ( c @ $false @ X2 @ X3 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f16,plain,
! [X2: $i,X3: $i] :
( ( c @ $false @ X2 @ X3 )
= ( sF3 @ X3 @ X2 ) ),
inference(reorient_equations,[],[f15]) ).
thf(f17,plain,
! [X2: $i,X3: $i] :
( ( sF3 @ X3 @ X2 )
= X3 ),
inference(definition_folding,[],[f9,f16]) ).
thf(f18,definition,
( sF4
= ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f19,plain,
( ( sK1 = sK0 )
= sF4 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,definition,
( sF5
= ( c @ sF4 @ sK1 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f21,plain,
( ( c @ sF4 @ sK1 @ sK0 )
= sF5 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,plain,
sK0 != sF5,
inference(definition_folding,[],[f8,f21,f19]) ).
thf(f23,plain,
( ( $false = sF4 )
| ( ( sK1 = sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f24,plain,
( ( ( sK1 = sK0 )
= $false )
| ( $true = sF4 ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f25,plain,
( ( $true = sF4 )
| ( sK1 != sK0 ) ),
inference(equality_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $false = sF4 )
| ( sK1 = sK0 ) ),
inference(equality_proxy_clausification,[],[f23]) ).
thf(f28,definition,
( spl6_1
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f29,plain,
( ( sK1 = sK0 )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f32,definition,
( spl6_2
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f34,plain,
( ( $true = sF4 )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f25,f32,f28]) ).
thf(f37,definition,
( spl6_3
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f39,plain,
( ( $false = sF4 )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl6_3
| spl6_1 ),
inference(avatar_split_clause,[],[f26,f28,f37]) ).
thf(f50,plain,
( ( ( c @ $false @ sK1 @ sK0 )
= sF5 )
| ~ spl6_3 ),
inference(forward_demodulation,[],[f21,f39]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( c @ $true @ X0 @ X1 )
= X0 ),
inference(forward_demodulation,[],[f13,f14]) ).
thf(f53,plain,
! [X2: $i,X3: $i] :
( ( c @ $false @ X2 @ X3 )
= X3 ),
inference(forward_demodulation,[],[f16,f17]) ).
thf(f55,plain,
( ( sK0 = sF5 )
| ~ spl6_3 ),
inference(constrained_superposition,[],[f50,f53]) ).
thf(f58,plain,
( $false
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f55,f22]) ).
thf(f59,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f58]) ).
thf(f61,plain,
( ( sF5
= ( c @ $true @ sK1 @ sK0 ) )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f21,f34]) ).
thf(f62,plain,
( ( sK1 = sF5 )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f61,f51]) ).
thf(f63,plain,
( ( sK0 = sF5 )
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_demodulation,[],[f62,f29]) ).
thf(f64,plain,
( $false
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f63,f22]) ).
thf(f65,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
( spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
~ spl6_3,
inference(sat_conversion,[],[f59]) ).
cnf(s5,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
spl6_1,
inference(rat,[],[s2,s4]) ).
cnf(s7,plain,
~ spl6_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6]) ).
thf(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO506^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:11:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.29 % (2397781)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (2397789)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=1654986701: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)
% 0.19/0.29 % (2397789)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397789)------------------------------
% 0.19/0.29 % (2397789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397789)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397789)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397789)Time elapsed: 0.001 s
% 0.19/0.29 % (2397789)Peak memory usage: 12 MB
% 0.19/0.29 % (2397789)Instructions burned: 1 (million)
% 0.19/0.29 % (2397789)------------------------------
% 0.19/0.29 % (2397789)------------------------------
% 0.19/0.29 % (2397786)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2632060949:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (2397787)lrs+10_16_si=on:nwc=1.5:random_seed=1760823950:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (2397788)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1082603070:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (2397788)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397788)------------------------------
% 0.19/0.29 % (2397788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397787)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397787)------------------------------
% 0.19/0.29 % (2397787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397786)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397786)------------------------------
% 0.19/0.29 % (2397786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397787)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397788)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397786)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397787)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397787)Time elapsed: 0.001 s
% 0.19/0.29 % (2397788)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397788)Time elapsed: 0.001 s
% 0.19/0.29 % (2397786)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397786)Time elapsed: 0.001 s
% 0.19/0.29 % (2397787)Peak memory usage: 12 MB
% 0.19/0.29 % (2397788)Peak memory usage: 12 MB
% 0.19/0.29 % (2397786)Peak memory usage: 12 MB
% 0.19/0.29 % (2397787)Instructions burned: 1 (million)
% 0.19/0.29 % (2397788)Instructions burned: 1 (million)
% 0.19/0.29 % (2397786)Instructions burned: 1 (million)
% 0.19/0.29 % (2397792)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.29 % (2397792)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
% 0.19/0.29 % (2397786)------------------------------
% 0.19/0.29 % (2397786)------------------------------
% 0.19/0.29 % (2397788)------------------------------
% 0.19/0.29 % (2397788)------------------------------
% 0.19/0.29 % (2397787)------------------------------
% 0.19/0.29 % (2397787)------------------------------
% 0.19/0.29 % (2397790)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3042166596:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (2397791)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3092798595:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.29 % (2397790)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397790)------------------------------
% 0.19/0.29 % (2397790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397790)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397790)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397790)Time elapsed: 0.001 s
% 0.19/0.29 % (2397790)Peak memory usage: 12 MB
% 0.19/0.29 % (2397790)Instructions burned: 1 (million)
% 0.19/0.29 % (2397790)------------------------------
% 0.19/0.29 % (2397790)------------------------------
% 0.19/0.29 % (2397792)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=3935108194:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.29 % (2397791)Refutation not found, incomplete strategy
% 0.19/0.29 % (2397791)------------------------------
% 0.19/0.29 % (2397791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397791)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397791)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (2397791)Time elapsed: 0.002 s
% 0.19/0.29 % (2397791)Peak memory usage: 12 MB
% 0.19/0.29 % (2397791)Instructions burned: 1 (million)
% 0.19/0.29 % (2397791)------------------------------
% 0.19/0.29 % (2397791)------------------------------
% 0.19/0.29 % (2397794)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3799490024:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.29 % (2397792) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2397781-2397792"...
% 0.19/0.29 % (2397794)Instruction limit reached!
% 0.19/0.29 % (2397794)------------------------------
% 0.19/0.29 % (2397794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397794)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397794)Termination reason: Instruction limit
% 0.19/0.29 % (2397794)Termination phase: Saturation
% 0.19/0.29 % (2397794)Time elapsed: 0.001 s
% 0.19/0.29 % (2397794)Peak memory usage: 11 MB
% 0.19/0.29 % (2397794)Instructions burned: 2 (million)
% 0.19/0.29 % (2397792)...printing done.
% 0.19/0.29 % (2397792)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (2397792)------------------------------
% 0.19/0.29 % (2397792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (2397792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (2397792)CaDiCaL version: 2.1.3
% 0.19/0.29 % (2397792)Termination reason: Refutation
% 0.19/0.29 % (2397792)Time elapsed: 0.004 s
% 0.19/0.29 % (2397792)Peak memory usage: 13 MB
% 0.19/0.29 % (2397792)Instructions burned: 4 (million)
% 0.19/0.29 % (2397781)Success in time 0.053 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------