%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG284^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 43 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 250 ( 8 ~; 0 |; 18 &; 221 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 ^; 63 !; 6 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cJ: $i > $i ).
thf(func_def_1,type,
cP: $i > $i > $i ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X0: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X3: $i,X4: $i] :
( ( cJ @ ( cP @ X3 @ X4 ) )
= ( cP @ ( cJ @ X4 ) @ ( cJ @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM18_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X0: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE ) )
=> ! [X3: $i,X4: $i] :
( ( cJ @ ( cP @ X3 @ X4 ) )
= ( cP @ ( cJ @ X4 ) @ ( cJ @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X3: $i,X2: $i] :
( ( cP @ X2 @ ( cP @ X1 @ X3 ) )
= ( cP @ ( cP @ X2 @ X1 ) @ X3 ) )
& ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) ) )
=> ! [X6: $i,X5: $i] :
( ( cJ @ ( cP @ X5 @ X6 ) )
= ( cP @ ( cJ @ X6 ) @ ( cJ @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ? [X6: $i,X5: $i] :
( ( cJ @ ( cP @ X5 @ X6 ) )
!= ( cP @ ( cJ @ X6 ) @ ( cJ @ X5 ) ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X1: $i,X3: $i,X2: $i] :
( ( cP @ X2 @ ( cP @ X1 @ X3 ) )
= ( cP @ ( cP @ X2 @ X1 ) @ X3 ) )
& ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ! [X4: $i] :
( cE
= ( cP @ ( cJ @ X4 ) @ X4 ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ? [X6: $i,X5: $i] :
( ( cJ @ ( cP @ X5 @ X6 ) )
!= ( cP @ ( cJ @ X6 ) @ ( cJ @ X5 ) ) )
& ! [X1: $i,X3: $i,X2: $i] :
( ( cP @ X2 @ ( cP @ X1 @ X3 ) )
= ( cP @ ( cP @ X2 @ X1 ) @ X3 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ? [X2: $i,X3: $i] :
( ( cJ @ ( cP @ X3 @ X2 ) )
!= ( cP @ ( cJ @ X2 ) @ ( cJ @ X3 ) ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( cP @ X6 @ ( cP @ X4 @ X5 ) )
= ( cP @ ( cP @ X6 @ X4 ) @ X5 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ( ( cP @ ( cJ @ sK0 ) @ ( cJ @ sK1 ) )
!= ( cJ @ ( cP @ sK1 @ sK0 ) ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( cP @ X6 @ ( cP @ X4 @ X5 ) )
= ( cP @ ( cP @ X6 @ X4 ) @ X5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f6]) ).
thf(f8,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( cP @ X6 @ ( cP @ X4 @ X5 ) )
= ( cP @ ( cP @ X6 @ X4 ) @ X5 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( cP @ ( cJ @ sK0 ) @ ( cJ @ sK1 ) )
!= ( cJ @ ( cP @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f8,f11]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f13,f10]) ).
thf(f19,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(constrained_superposition,[],[f16,f11]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ ( cJ @ X1 ) ) @ X0 )
= ( cP @ X1 @ X0 ) ),
inference(constrained_superposition,[],[f16,f16]) ).
thf(f23,plain,
! [X0: $i] :
( ( cP @ X0 @ cE )
= X0 ),
inference(forward_demodulation,[],[f19,f21]) ).
thf(f43,plain,
! [X0: $i] :
( cE
= ( cP @ X0 @ ( cJ @ X0 ) ) ),
inference(constrained_superposition,[],[f21,f11]) ).
thf(f70,plain,
! [X0: $i,X1: $i] :
( cE
= ( cP @ X0 @ ( cP @ X1 @ ( cJ @ ( cP @ X0 @ X1 ) ) ) ) ),
inference(constrained_superposition,[],[f8,f43]) ).
thf(f120,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ cE )
= ( cP @ X1 @ ( cJ @ ( cP @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f16,f70]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( cP @ X1 @ ( cJ @ ( cP @ X0 @ X1 ) ) )
= ( cJ @ X0 ) ),
inference(forward_demodulation,[],[f120,f23]) ).
thf(f179,plain,
! [X0: $i,X1: $i] :
( ( cJ @ ( cP @ X0 @ X1 ) )
= ( cP @ ( cJ @ X1 ) @ ( cJ @ X0 ) ) ),
inference(constrained_superposition,[],[f16,f132]) ).
thf(f267,plain,
( ( cJ @ ( cP @ sK1 @ sK0 ) )
!= ( cJ @ ( cP @ sK1 @ sK0 ) ) ),
inference(constrained_superposition,[],[f9,f179]) ).
thf(f271,plain,
$false,
inference(trivial_inequality_removal,[],[f267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG284^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:37:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.21/0.28 % (413556)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (413567)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (413567)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
% 0.21/0.28 % (413567)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=193342982:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (413561)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3328097094:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (413562)lrs+10_16_si=on:nwc=1.5:random_seed=3893876436:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (413564)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=2356376507: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)
% 0.21/0.28 % (413563)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1544151063:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (413565)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2940121677:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (413566)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4105803897:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (413563)Instruction limit reached!
% 0.21/0.28 % (413563)------------------------------
% 0.21/0.28 % (413563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (413563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (413563)CaDiCaL version: 2.1.3
% 0.21/0.28 % (413563)Termination reason: Instruction limit
% 0.21/0.28 % (413563)Termination phase: Saturation
% 0.21/0.28 % (413563)Time elapsed: 0.003 s
% 0.21/0.28 % (413563)Peak memory usage: 12 MB
% 0.21/0.28 % (413563)Instructions burned: 4 (million)
% 0.21/0.28 % (413562) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-413556-413562"...
% 0.21/0.28 % (413562)...printing done.
% 0.21/0.28 % (413562)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (413562)------------------------------
% 0.21/0.28 % (413562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (413562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (413562)CaDiCaL version: 2.1.3
% 0.21/0.28 % (413562)Termination reason: Refutation
% 0.21/0.28 % (413562)Time elapsed: 0.011 s
% 0.21/0.28 % (413562)Peak memory usage: 12 MB
% 0.21/0.28 % (413562)Instructions burned: 20 (million)
% 0.21/0.28 % (413556)Success in time 0.042 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------