%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 07:45:20 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 71 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 278 ( 9 ~; 0 |; 20 &; 231 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 6 con; 0-4 aty)
% ( 8 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 101 ( 33 ^; 58 !; 10 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGRP_RIGHT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_1,type,
cGRP_RIGHT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK0: g > g > g ).
thf(func_def_14,type,
sK1: g ).
thf(func_def_15,type,
sK2: g ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
sK3: g > g ).
thf(f1,axiom,
( cGRP_RIGHT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X2 @ X3 )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def) ).
thf(f2,axiom,
( cGRP_RIGHT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def) ).
thf(f3,conjecture,
! [X1: g,X0: g > g > g] :
( ( ! [X3: g,X2: g,X4: g] :
( ( X0 @ ( X0 @ X4 @ X2 ) @ X3 )
= ( X0 @ X4 @ ( X0 @ X2 @ X3 ) ) )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) )
=> ! [X4: g] :
( ( X0 @ X1 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE13A2A) ).
thf(f4,negated_conjecture,
~ ! [X1: g,X0: g > g > g] :
( ( ! [X3: g,X2: g,X4: g] :
( ( X0 @ ( X0 @ X4 @ X2 ) @ X3 )
= ( X0 @ X4 @ ( X0 @ X2 @ X3 ) ) )
& ( cGRP_RIGHT_UNIT @ X0 @ X1 )
& ( cGRP_RIGHT_INVERSE @ X0 @ X1 ) )
=> ! [X4: g] :
( ( X0 @ X1 @ X4 )
= X4 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ! [X2: g,X3: g,X4: g] :
( ( X1 @ X4 @ ( X1 @ X3 @ X2 ) )
= ( X1 @ ( X1 @ X4 @ X3 ) @ X2 ) )
& ( cGRP_RIGHT_UNIT @ X1 @ X0 )
& ( cGRP_RIGHT_INVERSE @ X1 @ X0 ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ! [X0: g,X1: g > g > g] :
( ( ( ( cGRP_RIGHT_UNIT @ X1 @ X0 )
= $true )
& ! [X4: g,X3: g,X2: g] :
( ( X1 @ X4 @ ( X1 @ X3 @ X2 ) )
= ( X1 @ ( X1 @ X4 @ X3 ) @ X2 ) )
& ( ( cGRP_RIGHT_INVERSE @ X1 @ X0 )
= $true ) )
=> ! [X5: g] :
( ( X1 @ X0 @ X5 )
= X5 ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
? [X0: g,X1: g > g > g] :
( ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 )
& ( ( cGRP_RIGHT_UNIT @ X1 @ X0 )
= $true )
& ! [X4: g,X3: g,X2: g] :
( ( X1 @ X4 @ ( X1 @ X3 @ X2 ) )
= ( X1 @ ( X1 @ X4 @ X3 ) @ X2 ) )
& ( ( cGRP_RIGHT_INVERSE @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f10,plain,
? [X1: g > g > g,X0: g] :
( ( ( cGRP_RIGHT_UNIT @ X1 @ X0 )
= $true )
& ? [X5: g] :
( ( X1 @ X0 @ X5 )
!= X5 )
& ! [X4: g,X3: g,X2: g] :
( ( X1 @ X4 @ ( X1 @ X3 @ X2 ) )
= ( X1 @ ( X1 @ X4 @ X3 ) @ X2 ) )
& ( ( cGRP_RIGHT_INVERSE @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
? [X0: g > g > g,X1: g] :
( ( ( cGRP_RIGHT_UNIT @ X0 @ X1 )
= $true )
& ? [X2: g] :
( ( X0 @ X1 @ X2 )
!= X2 )
& ! [X3: g,X4: g,X5: g] :
( ( X0 @ X3 @ ( X0 @ X4 @ X5 ) )
= ( X0 @ ( X0 @ X3 @ X4 ) @ X5 ) )
& ( ( cGRP_RIGHT_INVERSE @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( ( cGRP_RIGHT_UNIT @ sK0 @ sK1 )
= $true )
& ( ( sK0 @ sK1 @ sK2 )
!= sK2 )
& ! [X3: g,X4: g,X5: g] :
( ( sK0 @ ( sK0 @ X3 @ X4 ) @ X5 )
= ( sK0 @ X3 @ ( sK0 @ X4 @ X5 ) ) )
& ( ( cGRP_RIGHT_INVERSE @ sK0 @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f13,plain,
( ( cGRP_RIGHT_INVERSE @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f14,plain,
! [X3: g,X4: g,X5: g] :
( ( sK0 @ ( sK0 @ X3 @ X4 ) @ X5 )
= ( sK0 @ X3 @ ( sK0 @ X4 @ X5 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
( ( sK0 @ sK1 @ sK2 )
!= sK2 ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( ( cGRP_RIGHT_UNIT @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( cGRP_RIGHT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( cGRP_RIGHT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y2 @ Y1 )
= Y2 ) )
@ sK0
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f16,f18]) ).
thf(f22,plain,
( ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y2 @ Y3 )
= Y1 ) ) )
@ sK0
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f13,f17]) ).
thf(f23,plain,
( ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y0 @ Y1 )
= sK1 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: g] :
( ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ( sK0 @ X1 @ Y0 )
= sK1 )
@ ( sK3 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ ( sK3 @ X1 ) )
= sK1 )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X1: g] :
( sK1
= ( sK0 @ X1 @ ( sK3 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f30,plain,
! [X1: g] :
( ( ^ [Y0: g] :
( ( sK0 @ Y0 @ sK1 )
= Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X1: g] :
( ( ( sK0 @ X1 @ sK1 )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X1: g] :
( ( sK0 @ X1 @ sK1 )
= X1 ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X0: g,X1: g] :
( ( sK0 @ X0 @ ( sK0 @ sK1 @ X1 ) )
= ( sK0 @ X0 @ X1 ) ),
inference(constrained_superposition,[],[f14,f32]) ).
thf(f34,plain,
! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ ( sK3 @ X0 ) @ X1 ) ) ),
inference(constrained_superposition,[],[f14,f28]) ).
thf(f57,plain,
! [X0: g] :
( ( sK0 @ sK1 @ ( sK3 @ ( sK3 @ X0 ) ) )
= ( sK0 @ X0 @ sK1 ) ),
inference(constrained_superposition,[],[f34,f28]) ).
thf(f66,plain,
! [X0: g] :
( ( sK0 @ sK1 @ ( sK3 @ ( sK3 @ X0 ) ) )
= X0 ),
inference(forward_demodulation,[],[f57,f32]) ).
thf(f73,plain,
! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ X1 @ ( sK3 @ ( sK3 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f33,f66]) ).
thf(f75,plain,
! [X0: g] :
( ( sK0 @ sK1 @ X0 )
= X0 ),
inference(backward_demodulation,[],[f66,f73]) ).
thf(f76,plain,
sK2 != sK2,
inference(backward_demodulation,[],[f15,f75]) ).
thf(f80,plain,
$false,
inference(trivial_inequality_removal,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG279^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n016.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 17:41:05 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.30 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
% 0.24/0.35 % (671606)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.35 % (671616)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1562667124:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.35 % (671617)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.35 % (671617)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
% 0.24/0.35 % (671616) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-671606-671616"...
% 0.24/0.35 % (671612)lrs+10_16_si=on:nwc=1.5:random_seed=3763524134:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.35 % (671611)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2380789105:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.35 % (671616)...printing done.
% 0.24/0.35 % (671617)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=973596274:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.35 % (671613)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=602762095:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.35 % (671616)Refutation found. Thanks to Tanya!
% 0.24/0.35 % SZS status Theorem for theBenchmark
% 0.24/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.35 % (671616)------------------------------
% 0.24/0.35 % (671616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (671616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (671616)CaDiCaL version: 2.1.3
% 0.24/0.35 % (671616)Termination reason: Refutation
% 0.24/0.35 % (671616)Time elapsed: 0.006 s
% 0.24/0.35 % (671616)Peak memory usage: 12 MB
% 0.24/0.35 % (671616)Instructions burned: 9 (million)
% 0.24/0.35 % (671606)Success in time 0.037 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------