%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : QUA006^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:21:23 AM UTC 2026
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 327 ( 127 equ; 4 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 466 ( 3 ~; 0 |; 30 &; 370 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 28 usr; 8 con; 0-4 aty)
% ( 19 !!; 44 ??; 0 @@+; 0 @@-)
% Number of variables : 157 ( 116 ^; 37 !; 4 ?; 157 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vIFF: $o > $o > $o ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vAND: $o > $o > $o ).
thf(func_def_25,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
db5:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',emptyset_def) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',singleton_def) ).
thf(f4,axiom,
( ( sup @ emptyset )
= zero ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',sup_es) ).
thf(f5,axiom,
! [X0: $i] :
( ( sup @ ( singleton @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',sup_singleset) ).
thf(f11,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i,X4: $i] :
( ( X2
= ( multiplication @ X3 @ X4 ) )
& ( X0 @ X3 )
& ( X1 @ X4 ) ) )
= crossmult ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',crossmult_def) ).
thf(f12,axiom,
! [X1: $i > $o,X0: $i > $o] :
( ( multiplication @ ( sup @ X0 ) @ ( sup @ X1 ) )
= ( sup @ ( crossmult @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',multiplication_def) ).
thf(f13,axiom,
! [X0: $i] :
( ( multiplication @ X0 @ one )
= X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',multiplication_neutral_right) ).
thf(f15,conjecture,
! [X0: $i] :
( ( multiplication @ zero @ X0 )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_anni) ).
thf(f16,negated_conjecture,
~ ! [X0: $i] :
( ( multiplication @ zero @ X0 )
= zero ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f21,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i,X4: $i] :
( ( X2
= ( multiplication @ X3 @ X4 ) )
& ( X0 @ X3 )
& ( X1 @ X4 ) ) )
= crossmult ),
inference(rectify,[],[f11]) ).
thf(f22,plain,
( crossmult
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y4 )
& ( ( multiplication @ Y4 @ Y3 )
= Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( sup @ emptyset )
= zero ),
inference(fool_elimination,[],[f4]) ).
thf(f25,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( multiplication @ Y0 @ one )
= Y0 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f26,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f1]) ).
thf(f32,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sup @ ( singleton @ Y0 ) )
= Y0 ) )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f33,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( zero
= ( multiplication @ zero @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f35,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f36,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( multiplication @ ( sup @ X1 ) @ ( sup @ X0 ) )
= ( sup @ ( crossmult @ X1 @ X0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f37,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( multiplication @ ( sup @ Y0 ) @ ( sup @ Y1 ) )
= ( sup @ ( crossmult @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f40,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( multiplication @ Y0 @ one )
= Y0 ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f42,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sup @ ( singleton @ Y0 ) )
= Y0 ) )
= $true ),
inference(cnf_transformation,[],[f32]) ).
thf(f44,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( multiplication @ ( sup @ Y0 ) @ ( sup @ Y1 ) )
= ( sup @ ( crossmult @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f37]) ).
thf(f45,plain,
( ( sup @ emptyset )
= zero ),
inference(cnf_transformation,[],[f23]) ).
thf(f48,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( zero
= ( multiplication @ zero @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f50,plain,
( crossmult
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y4 )
& ( ( multiplication @ Y4 @ Y3 )
= Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f56,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sup
@ ( ^ [Y1: $i,Y2: $i] : ( Y1 = Y2 )
@ Y0 ) )
= Y0 ) ) ),
inference(definition_unfolding,[],[f43,f38]) ).
thf(f57,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( multiplication @ ( sup @ Y0 ) @ ( sup @ Y1 ) )
= ( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ?? @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y5 )
& ( Y2 @ Y6 )
& ( ( multiplication @ Y6 @ Y5 )
= Y4 ) ) ) )
@ Y0
@ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f44,f50]) ).
thf(f58,plain,
( zero
= ( sup
@ ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f45,f42]) ).
thf(f62,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sup @ ( (=) @ Y0 ) )
= Y0 ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f64,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( multiplication @ ( sup @ Y0 ) @ ( sup @ Y1 ) )
= ( sup
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y4 )
& ( ( multiplication @ Y4 @ Y3 )
= Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f65,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( zero
= ( multiplication @ zero @ Y0 ) ) )
= $false ),
inference(not_proxy_clausification,[],[f48]) ).
thf(f66,plain,
( ( ^ [Y0: $i] :
( zero
= ( multiplication @ zero @ Y0 ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( zero
= ( multiplication @ zero @ sK0 ) )
= $false ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f71,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( multiplication @ Y0 @ one )
= Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f72,plain,
! [X1: $i] :
( ( ( multiplication @ X1 @ one )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( ( multiplication @ X1 @ one )
= X1 ),
inference(equality_proxy_clausification,[],[f72]) ).
thf(f85,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sup @ ( (=) @ Y0 ) )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f86,plain,
! [X1: $i] :
( ( ( sup @ ( (=) @ X1 ) )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X1: $i] :
( ( sup @ ( (=) @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[],[f86]) ).
thf(f102,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( multiplication @ ( sup @ Y0 ) @ ( sup @ Y1 ) )
= ( sup
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 )
& ( Y0 @ Y4 )
& ( ( multiplication @ Y4 @ Y3 )
= Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f103,plain,
! [X1: $i > $o] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( multiplication @ ( sup @ X1 ) @ ( sup @ Y0 ) )
= ( sup
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 )
& ( X1 @ Y3 )
& ( ( multiplication @ Y3 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( multiplication @ ( sup @ X1 ) @ ( sup @ Y0 ) )
= ( sup
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 )
& ( X1 @ Y3 )
& ( ( multiplication @ Y3 @ Y2 )
= Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i > $o,X1: $i > $o] :
( $true
= ( ( multiplication @ ( sup @ X1 ) @ ( sup @ X2 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( X2 @ Y1 )
& ( X1 @ Y2 )
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f107,plain,
! [X0: $i > $o] :
( ( ( multiplication @ ( sup @ X0 ) @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i] : $false
@ Y1 )
& ( X0 @ Y2 )
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(constrained_superposition,[],[f105,f58]) ).
thf(f110,plain,
! [X0: $i > $o] :
( $true
= ( ( multiplication @ zero @ ( sup @ X0 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 )
& ( ^ [Y3: $i] : $false
@ Y2 )
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f105,f58]) ).
thf(f113,plain,
! [X0: $i > $o] :
( $true
= ( ( multiplication @ zero @ ( sup @ X0 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( X0 @ Y1 )
& $false
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f114,plain,
! [X0: $i > $o] :
( ( ( multiplication @ zero @ ( sup @ X0 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( $false
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f113]) ).
thf(f115,plain,
! [X0: $i > $o] :
( ( ( multiplication @ zero @ ( sup @ X0 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) )
= $true ),
inference(boolean_simplification,[],[f114]) ).
thf(f117,plain,
! [X0: $i > $o] :
( ( ( multiplication @ ( sup @ X0 ) @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( $false
& ( X0 @ Y2 )
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f118,plain,
! [X0: $i > $o] :
( $true
= ( ( multiplication @ ( sup @ X0 ) @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( $false
& ( ( multiplication @ Y2 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f117]) ).
thf(f119,plain,
! [X0: $i > $o] :
( $true
= ( ( multiplication @ ( sup @ X0 ) @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ) ),
inference(boolean_simplification,[],[f118]) ).
thf(f121,plain,
! [X0: $i > $o] :
( ( multiplication @ zero @ ( sup @ X0 ) )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ),
inference(equality_proxy_clausification,[],[f115]) ).
thf(f122,plain,
( $true
= ( ( multiplication @ zero @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ) ),
inference(constrained_superposition,[],[f115,f58]) ).
thf(f127,plain,
! [X0: $i] :
( ( multiplication @ zero @ X0 )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ),
inference(constrained_superposition,[],[f121,f87]) ).
thf(f138,plain,
! [X0: $i] :
( ( multiplication @ zero @ X0 )
= ( multiplication @ zero @ ( multiplication @ zero @ X0 ) ) ),
inference(constrained_superposition,[],[f121,f127]) ).
thf(f145,plain,
( zero
= ( multiplication @ zero @ zero ) ),
inference(constrained_superposition,[],[f138,f73]) ).
thf(f179,plain,
( $true
= ( zero
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ) ),
inference(constrained_superposition,[],[f122,f145]) ).
thf(f180,plain,
( zero
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ),
inference(equality_proxy_clausification,[],[f179]) ).
thf(f212,plain,
! [X0: $i > $o] :
( ( multiplication @ ( sup @ X0 ) @ zero )
= ( sup
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : $false ) ) ) ),
inference(equality_proxy_clausification,[],[f119]) ).
thf(f216,plain,
! [X0: $i] :
( ( ( multiplication @ ( multiplication @ zero @ X0 ) @ zero )
= ( multiplication @ zero @ X0 ) )
= $true ),
inference(constrained_superposition,[],[f119,f127]) ).
thf(f220,plain,
! [X0: $i > $o] :
( zero
= ( multiplication @ ( sup @ X0 ) @ zero ) ),
inference(forward_demodulation,[],[f212,f180]) ).
thf(f228,plain,
! [X0: $i] :
( zero
= ( multiplication @ X0 @ zero ) ),
inference(constrained_superposition,[],[f220,f87]) ).
thf(f259,plain,
! [X0: $i] :
( ( multiplication @ zero @ X0 )
= ( multiplication @ ( multiplication @ zero @ X0 ) @ zero ) ),
inference(equality_proxy_clausification,[],[f216]) ).
thf(f269,plain,
! [X0: $i] :
( zero
= ( multiplication @ zero @ X0 ) ),
inference(forward_demodulation,[],[f259,f228]) ).
thf(f291,plain,
( ( zero = zero )
= $false ),
inference(constrained_superposition,[],[f68,f269]) ).
thf(f294,plain,
$true = $false,
inference(boolean_simplification,[],[f291]) ).
thf(f295,plain,
$false,
inference(trivial_inequality_removal,[],[f294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA006^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:24:37 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.39 % (321562)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.39 % (321573)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.39 % (321573)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
% 0.22/0.39 % (321573)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=832286464:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.39 % (321573)Refutation not found, incomplete strategy
% 0.22/0.39 % (321573)------------------------------
% 0.22/0.39 % (321573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321573)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321573)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39 % (321573)Time elapsed: 0.006 s
% 0.22/0.39 % (321573)Peak memory usage: 12 MB
% 0.22/0.39 % (321573)Instructions burned: 5 (million)
% 0.22/0.39 % (321573)------------------------------
% 0.22/0.39 % (321573)------------------------------
% 0.22/0.39 % (321569)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2788930831:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.39 % (321571)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3579490921:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.39 % (321569)Instruction limit reached!
% 0.22/0.39 % (321569)------------------------------
% 0.22/0.39 % (321569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321569)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321569)Termination reason: Instruction limit
% 0.22/0.39 % (321569)Termination phase: Saturation
% 0.22/0.39 % (321569)Time elapsed: 0.003 s
% 0.22/0.39 % (321569)Peak memory usage: 11 MB
% 0.22/0.39 % (321569)Instructions burned: 3 (million)
% 0.22/0.39 % (321570)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=3885183841: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)
% 0.22/0.39 % (321571)Instruction limit reached!
% 0.22/0.39 % (321571)------------------------------
% 0.22/0.39 % (321571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321571)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321571)Termination reason: Instruction limit
% 0.22/0.39 % (321571)Termination phase: Saturation
% 0.22/0.39 % (321571)Time elapsed: 0.013 s
% 0.22/0.39 % (321571)Peak memory usage: 12 MB
% 0.22/0.39 % (321571)Instructions burned: 24 (million)
% 0.22/0.39 % (321568)lrs+10_16_si=on:nwc=1.5:random_seed=2032639217:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (321567)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=154603996:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.39 % (321572)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2328700655:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.39 % (321567)Refutation not found, incomplete strategy
% 0.22/0.39 % (321567)------------------------------
% 0.22/0.39 % (321567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321567)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321567)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39 % (321567)Time elapsed: 0.005 s
% 0.22/0.39 % (321567)Peak memory usage: 12 MB
% 0.22/0.39 % (321567)Instructions burned: 4 (million)
% 0.22/0.39 % (321567)------------------------------
% 0.22/0.39 % (321567)------------------------------
% 0.22/0.39 % (321575)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1557914882:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (321580)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.39 % (321575)Instruction limit reached!
% 0.22/0.39 % (321575)------------------------------
% 0.22/0.39 % (321575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321575)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321575)Termination reason: Instruction limit
% 0.22/0.39 % (321575)Termination phase: Saturation
% 0.22/0.39 % (321575)Time elapsed: 0.003 s
% 0.22/0.39 % (321575)Peak memory usage: 11 MB
% 0.22/0.39 % (321575)Instructions burned: 3 (million)
% 0.22/0.39 % (321580)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=457719395:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.39 % (321578)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3044620825:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.39 % (321580)Instruction limit reached!
% 0.22/0.39 % (321580)------------------------------
% 0.22/0.39 % (321580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321580)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321580)Termination reason: Instruction limit
% 0.22/0.39 % (321580)Termination phase: Saturation
% 0.22/0.39 % (321580)Time elapsed: 0.004 s
% 0.22/0.39 % (321580)Peak memory usage: 12 MB
% 0.22/0.39 % (321580)Instructions burned: 7 (million)
% 0.22/0.39 % (321568)Instruction limit reached!
% 0.22/0.39 % (321568)------------------------------
% 0.22/0.39 % (321568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321568)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321568)Termination reason: Instruction limit
% 0.22/0.39 % (321568)Termination phase: Saturation
% 0.22/0.39 % (321568)Time elapsed: 0.018 s
% 0.22/0.39 % (321568)Peak memory usage: 12 MB
% 0.22/0.39 % (321568)Instructions burned: 18 (million)
% 0.22/0.39 % (321578)Instruction limit reached!
% 0.22/0.39 % (321578)------------------------------
% 0.22/0.39 % (321578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321578)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321578)Termination reason: Instruction limit
% 0.22/0.39 % (321578)Termination phase: Saturation
% 0.22/0.39 % (321578)Time elapsed: 0.005 s
% 0.22/0.39 % (321578)Peak memory usage: 12 MB
% 0.22/0.39 % (321578)Instructions burned: 5 (million)
% 0.22/0.39 % (321589)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3674869644:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.39 % (321587)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
% 0.22/0.39 % (321587)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.39 % (321585)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2607883679:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.39 % (321587)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2885855581:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.39 % (321591)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.39 % (321589) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-321562-321589"...
% 0.22/0.39 % (321590)lrs+10_1_si=on:cs=on:random_seed=4241529030:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.39 % (321589)...printing done.
% 0.22/0.39 % (321591)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2634645703:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (321585)Instruction limit reached!
% 0.22/0.39 % (321585)------------------------------
% 0.22/0.39 % (321585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321585)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321585)Termination reason: Instruction limit
% 0.22/0.39 % (321585)Termination phase: Saturation
% 0.22/0.39 % (321585)Time elapsed: 0.014 s
% 0.22/0.39 % (321585)Peak memory usage: 12 MB
% 0.22/0.39 % (321585)Instructions burned: 13 (million)
% 0.22/0.39 % (321591)Instruction limit reached!
% 0.22/0.39 % (321591)------------------------------
% 0.22/0.39 % (321591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321591)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321591)Termination reason: Instruction limit
% 0.22/0.39 % (321591)Termination phase: Property scanning
% 0.22/0.39 % (321591)Time elapsed: 0.002 s
% 0.22/0.39 % (321591)Peak memory usage: 10 MB
% 0.22/0.39 % (321591)Instructions burned: 2 (million)
% 0.22/0.39 % (321589)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (321589)------------------------------
% 0.22/0.39 % (321589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.39 % (321589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.39 % (321589)CaDiCaL version: 2.1.3
% 0.22/0.39 % (321589)Termination reason: Refutation
% 0.22/0.39 % (321589)Time elapsed: 0.016 s
% 0.22/0.39 % (321589)Peak memory usage: 12 MB
% 0.22/0.39 % (321589)Instructions burned: 31 (million)
% 0.22/0.39 % (321562)Success in time 0.138 s
% 0.22/0.39 % Vampire exiting
%------------------------------------------------------------------------------