%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : QUA002^1 : 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 : n012.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 08:21:22 AM UTC 2026
% Result : Theorem 0.06s 0.17s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 322 ( 127 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 156 ( 21 ~; 53 |; 0 &; 80 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-4 aty)
% Number of variables : 69 ( 0 sgn 6 !; 2 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
emptyset: $i > $o ).
thf(func_def_1,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
singleton: $i > $i > $o ).
thf(func_def_5,type,
sup: ( $i > $o ) > $i ).
thf(func_def_6,type,
supset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
unionset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
addition: $i > $i > $i ).
thf(func_def_9,type,
leq: $i > $i > $o ).
thf(func_def_10,type,
multiplication: $i > $i > $i ).
thf(func_def_11,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(f2,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/QUA001^0.ax',union_def) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) )
= singleton ),
file('/export/starexec/sandbox2/benchmark/Axioms/QUA001^0.ax',singleton_def) ).
thf(f9,axiom,
( ( ^ [X0: $i,X1: $i] : ( sup @ ( union @ ( singleton @ X0 ) @ ( singleton @ X1 ) ) ) )
= addition ),
file('/export/starexec/sandbox2/benchmark/Axioms/QUA001^0.ax',addition_def) ).
thf(f15,conjecture,
! [X1: $i,X0: $i] :
( ( addition @ X0 @ X1 )
= ( addition @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_comm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( addition @ X0 @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f24,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f25,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] : ( sup @ ( union @ ( singleton @ Y0 ) @ ( singleton @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f28,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f29,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f31,plain,
~ ! [X0: $i,X1: $i] :
( ( addition @ X0 @ X1 )
= ( addition @ X1 @ X0 ) ),
inference(rectify,[],[f16]) ).
thf(f32,plain,
? [X0: $i,X1: $i] :
( ( addition @ X0 @ X1 )
!= ( addition @ X1 @ X0 ) ),
inference(ennf_transformation,[],[f31]) ).
thf(f35,plain,
( ( addition @ sK1 @ sK0 )
!= ( addition @ sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
thf(f40,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f47,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] : ( sup @ ( union @ ( singleton @ Y0 ) @ ( singleton @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f48,plain,
( ( addition @ sK1 @ sK0 )
!= ( addition @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f49,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f54,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] :
( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y0 )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f47,f40,f49,f49]) ).
thf(f60,plain,
( ( ^ [Y0: $i,Y1: $i] :
( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y0 )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) )
@ sK1
@ sK0 )
!= ( ^ [Y0: $i,Y1: $i] :
( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y0 )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f48,f54,f54]) ).
thf(f65,plain,
( ( sup
@ ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) ) )
!= ( sup
@ ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f68,plain,
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) ) ) ),
inference(equality_resolution,[],[f65]) ).
thf(f76,plain,
( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 )
!= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f68]) ).
thf(f77,plain,
( ( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( ( ^ [Y0: $i] :
( ( sK1 = Y0 )
| ( sK0 = Y0 ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f76]) ).
thf(f79,plain,
( ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $false )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
( ( ( sK0 = sK2 )
= $false )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $false )
| ( ( sK1 = sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f79]) ).
thf(f82,plain,
( ( ( sK1 = sK2 )
= $false )
| ( ( sK1 = sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f81]) ).
thf(f86,plain,
( ( sK1 != sK2 )
| ( sK1 != sK2 ) ),
inference(equality_proxy_clausification,[],[f82]) ).
thf(f87,plain,
sK1 != sK2,
inference(duplicate_literal_removal,[],[f86]) ).
thf(f88,plain,
( ( sK0 != sK2 )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f80]) ).
thf(f90,plain,
( ( sK0 != sK2 )
| ( ( sK0 = sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f88]) ).
thf(f91,plain,
( ( sK0 != sK2 )
| ( sK0 != sK2 ) ),
inference(equality_proxy_clausification,[],[f90]) ).
thf(f92,plain,
sK0 != sK2,
inference(duplicate_literal_removal,[],[f91]) ).
thf(f94,plain,
( ( ( ( sK1 = sK2 )
| ( sK0 = sK2 ) )
= $true )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f95,plain,
( ( ( sK1 = sK2 )
= $true )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $true )
| ( ( sK0 = sK2 )
= $true ) ),
inference(or_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( sK1 = sK2 )
| ( ( ( sK0 = sK2 )
| ( sK1 = sK2 ) )
= $true )
| ( ( sK0 = sK2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( ( ( sK1 = sK2 )
= $true )
| ( ( sK0 = sK2 )
= $true )
| ( sK1 = sK2 )
| ( ( sK0 = sK2 )
= $true ) ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( ( sK0 = sK2 )
= $true )
| ( ( sK0 = sK2 )
= $true ) ),
inference(equality_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( ( sK1 = sK2 )
| ( sK1 = sK2 )
| ( sK0 = sK2 )
| ( sK0 = sK2 ) ),
inference(equality_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( sK1 = sK2 )
| ( sK0 = sK2 ) ),
inference(duplicate_literal_removal,[],[f99]) ).
thf(f102,definition,
( spl3_1
<=> ( sK0 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f105,definition,
( spl3_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f108,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f87,f105]) ).
thf(f109,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f92,f102]) ).
thf(f113,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f100,f105,f102]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f108]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f113]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6]) ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : QUA002^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:28:41 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.17 % (96448)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.17 % (96465)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.17 % (96465)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
% 0.06/0.17 % (96461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1352333975:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.17 % (96462)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=3329999662: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)
% 0.06/0.17 % (96463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1857962135:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.17 % (96459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4091521670:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.17 % (96460)lrs+10_16_si=on:nwc=1.5:random_seed=3869478157:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.17 % (96465)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=1716363625:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.17 % (96464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2859462165:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.17 % (96461)Instruction limit reached!
% 0.06/0.17 % (96461)------------------------------
% 0.06/0.17 % (96461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (96461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (96461)CaDiCaL version: 2.1.3
% 0.06/0.17 % (96461)Termination reason: Instruction limit
% 0.06/0.17 % (96461)Termination phase: Saturation
% 0.06/0.17 % (96461)Time elapsed: 0.001 s
% 0.06/0.17 % (96461)Peak memory usage: 11 MB
% 0.06/0.17 % (96461)Instructions burned: 3 (million)
% 0.06/0.17 % (96459)Refutation not found, incomplete strategy
% 0.06/0.17 % (96459)------------------------------
% 0.06/0.17 % (96459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (96459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (96459)CaDiCaL version: 2.1.3
% 0.06/0.17 % (96459)Termination reason: Refutation not found, incomplete strategy
% 0.06/0.17 % (96459)Time elapsed: 0.002 s
% 0.06/0.17 % (96459)Peak memory usage: 12 MB
% 0.06/0.17 % (96459)Instructions burned: 5 (million)
% 0.06/0.17 % (96465)Refutation not found, incomplete strategy
% 0.06/0.17 % (96465)------------------------------
% 0.06/0.17 % (96465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.17 % (96465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.17 % (96465)CaDiCaL version: 2.1.3
% 0.06/0.17 % (96465)Termination reason: Refutation not found, incomplete strategy
% 0.06/0.17 % (96465)Time elapsed: 0.002 s
% 0.06/0.17 % (96465)Peak memory usage: 12 MB
% 0.06/0.17 % (96465)Instructions burned: 6 (million)
% 0.06/0.17 % (96459)------------------------------
% 0.06/0.17 % (96459)------------------------------
% 0.06/0.17 % (96464) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-96448-96464"...
% 0.06/0.17 % (96465)------------------------------
% 0.06/0.17 % (96465)------------------------------
% 0.06/0.17 % (96464)...printing done.
% 0.06/0.17 % (96464)Refutation found. Thanks to Tanya!
% 0.06/0.17 % SZS status Theorem for theBenchmark
% 0.06/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.18 % (96464)------------------------------
% 0.06/0.18 % (96464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.18 % (96464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.18 % (96464)CaDiCaL version: 2.1.3
% 0.06/0.18 % (96464)Termination reason: Refutation
% 0.06/0.18 % (96464)Time elapsed: 0.003 s
% 0.06/0.18 % (96464)Peak memory usage: 13 MB
% 0.06/0.18 % (96464)Instructions burned: 8 (million)
% 0.06/0.18 % (96448)Success in time 0.032 s
% 0.06/0.18 % Vampire exiting
%------------------------------------------------------------------------------