%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET592^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:23:18 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 192 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 178 ( 22 ~; 20 |; 35 &; 86 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 85 ( 36 ^; 40 !; 9 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a > $o ).
thf(func_def_9,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( X0
= ( ^ [X3: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_51_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] : $false ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( X0
= ( ^ [X3: a] : $false ) ) ),
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] : $false ) )
& ! [X6: a] :
( ( X1 @ X6 )
=> ( X0 @ X6 ) ) )
=> ( X1
= ( ^ [X7: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X6: a] :
( ( ( X1 @ X6 )
= $true )
=> ( ( X0 @ X6 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
=> ( ( X0 @ X4 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) ) )
=> ( ( ^ [Y0: a] : $false )
= X1 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X1 )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
| ( $true
!= ( X1 @ X4 ) ) )
& ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X1: a > $o,X2: a > $o,X0: a > $o] :
( ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
| ( $true
!= ( X1 @ X4 ) ) )
& ( ( ^ [Y0: a] :
( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( ^ [Y0: a] : $false )
!= X1 ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
& ( ( ^ [Y0: a] : $false )
!= X0 ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X3: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( sK2 @ X4 )
= $true )
| ( ( sK0 @ X4 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( sK0
!= ( ^ [Y0: a] : $false ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
( sK0
!= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X4: a] :
( ( ( sK0 @ X4 )
!= $true )
| ( ( sK2 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X3: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( ( sK1 @ X3 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( sK0 @ sK3 )
!= ( ^ [Y0: a] : $false
@ sK3 ) ),
inference(negative_extensionality,[],[f10]) ).
thf(f17,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ^ [Y0: a] : $false
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f20,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $false = $true ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f21,plain,
( ( sK0 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
( ( $true != $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f12,f21]) ).
thf(f23,plain,
( ( sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( ( $true != $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f13,f21]) ).
thf(f25,plain,
( ( sK1 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f26,plain,
! [X1: a] :
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) ),
inference(argument_congruence,[],[f11]) ).
thf(f28,plain,
! [X1: a] :
( ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: a] : $false
@ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f29,plain,
! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( sK1 @ X1 )
& ( sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: a] :
( ( $false = $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f35,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f31,f25]) ).
thf(f37,plain,
( ( sK2 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f39,plain,
$false = $true,
inference(forward_demodulation,[],[f37,f23]) ).
thf(f40,plain,
$false,
inference(trivial_inequality_removal,[],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET592^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:40:14 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 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
% 0.10/0.25 % (2509849)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (2509859)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2184892314:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.25 % (2509859)Refutation not found, incomplete strategy
% 0.10/0.25 % (2509859)------------------------------
% 0.10/0.25 % (2509859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2509859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2509859)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2509859)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.25 % (2509859)Time elapsed: 0.001 s
% 0.10/0.25 % (2509859)Peak memory usage: 12 MB
% 0.10/0.25 % (2509859)Instructions burned: 1 (million)
% 0.10/0.25 % (2509859)------------------------------
% 0.10/0.25 % (2509859)------------------------------
% 0.10/0.25 % (2509863)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.25 % (2509863)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
% 0.10/0.25 % (2509857)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2133393411:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.10/0.25 % (2509861)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2807798236:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.10/0.25 % (2509860)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=39702657: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)
% 0.10/0.25 % (2509862)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2950260107:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.10/0.25 % (2509863)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=3008408625:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.10/0.25 % (2509858)lrs+10_16_si=on:nwc=1.5:random_seed=3399793854:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.10/0.25 % (2509857) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509857"...
% 0.10/0.25 % (2509861) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509861"...
% 0.10/0.25 % (2509862) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509862"...
% 0.10/0.25 % (2509860) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509860"...
% 0.10/0.25 % (2509858) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509858"...
% 0.10/0.25 % (2509861)...printing done.
% 0.10/0.25 % (2509857)...printing done.
% 0.10/0.25 % (2509865)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=416844008:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.10/0.25 % (2509863) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2509849-2509863"...
% 0.10/0.25 % (2509862)...printing done.
% 0.10/0.25 % (2509860)...printing done.
% 0.10/0.25 % (2509858)...printing done.
% 0.10/0.25 % (2509865)Instruction limit reached!
% 0.10/0.25 % (2509865)------------------------------
% 0.10/0.25 % (2509865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2509865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2509865)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2509865)Termination reason: Instruction limit
% 0.10/0.25 % (2509865)Termination phase: Saturation
% 0.10/0.25 % (2509865)Time elapsed: 0.001 s
% 0.10/0.25 % (2509865)Peak memory usage: 12 MB
% 0.10/0.25 % (2509865)Instructions burned: 2 (million)
% 0.10/0.25 % (2509857)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (2509857)------------------------------
% 0.10/0.25 % (2509857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (2509857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (2509857)CaDiCaL version: 2.1.3
% 0.10/0.25 % (2509857)Termination reason: Refutation
% 0.10/0.25 % (2509857)Time elapsed: 0.003 s
% 0.10/0.25 % (2509857)Peak memory usage: 12 MB
% 0.10/0.25 % (2509857)Instructions burned: 3 (million)
% 0.10/0.25 % (2509849)Success in time 0.027 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------