%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP209^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:08:52 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 258 ( 5 ~; 0 |; 6 &; 223 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 40 usr; 6 con; 0-4 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 31 ^; 27 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
syntax_ac_operator_a: ( a > a > a ) > $o ).
thf(func_def_1,type,
a2: a ).
thf(func_def_2,type,
b: a ).
thf(func_def_3,type,
c: a ).
thf(func_def_4,type,
f: a > a > a ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK0: ( a > a > a ) > a ).
thf(func_def_17,type,
sK1: ( a > a > a ) > a ).
thf(func_def_18,type,
sK2: ( a > a > a ) > a ).
thf(func_def_19,type,
sK3: ( a > a > a ) > a ).
thf(func_def_20,type,
sK4: ( a > a > a ) > a ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
sK5: ( a > a > a ) > a ).
thf(func_def_23,type,
sK6: ( a > a > a ) > a ).
thf(func_def_24,type,
sK7: ( a > a > a ) > a ).
thf(func_def_25,type,
sK8: ( a > a > a ) > a ).
thf(func_def_26,type,
sK9: ( a > a > a ) > a ).
thf(func_def_27,type,
sK10: ( a > a > a ) > a ).
thf(func_def_28,type,
sK11: ( a > a > a ) > a ).
thf(func_def_29,type,
sK12: ( a > a > a ) > a ).
thf(func_def_30,type,
sK13: ( a > a > a ) > a ).
thf(func_def_31,type,
sK14: ( a > a > a ) > a ).
thf(func_def_32,type,
sK15: ( a > a > a ) > a ).
thf(func_def_33,type,
sK16: ( a > a > a ) > a ).
thf(func_def_34,type,
sK17: ( a > a > a ) > a ).
thf(func_def_35,type,
sK18: ( a > a > a ) > a ).
thf(func_def_36,type,
sK19: ( a > a > a ) > a ).
thf(func_def_37,type,
sK20: ( a > a > a ) > a ).
thf(func_def_38,type,
sK21: ( a > a > a ) > a ).
thf(func_def_39,type,
sK22: ( a > a > a ) > a ).
thf(func_def_40,type,
sK23: ( a > a > a ) > a ).
thf(func_def_41,type,
sK24: ( a > a > a ) > a ).
thf(f1,axiom,
syntax_ac_operator_a @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(f4,axiom,
! [X1: a,X0: a,X2: a] :
( ( f @ ( f @ X0 @ X1 ) @ X2 )
= ( f @ X0 @ ( f @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(f10,axiom,
( syntax_ac_operator_a
= ( ^ [X0: a > a > a] :
( ! [X2: a,X3: a,X1: a] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) )
& ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
= ( X0 @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ac__operator__def) ).
thf(f11,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f12,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f23,plain,
( syntax_ac_operator_a
= ( ^ [X0: a > a > a] :
( ! [X1: a,X2: a,X3: a] :
( ( X0 @ X3 @ ( X0 @ X1 @ X2 ) )
= ( X0 @ ( X0 @ X3 @ X1 ) @ X2 ) )
& ! [X4: a,X5: a] :
( ( X0 @ X5 @ X4 )
= ( X0 @ X4 @ X5 ) ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f24,plain,
( syntax_ac_operator_a
= ( ^ [Y0: a > a > a] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
syntax_ac_operator_a @ f,
inference(rectify,[],[f1]) ).
thf(f26,plain,
( ( syntax_ac_operator_a @ f )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f28,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(flattening,[],[f12]) ).
thf(f36,plain,
! [X0: a,X1: a,X2: a] :
( ( f @ X1 @ ( f @ X0 @ X2 ) )
= ( f @ ( f @ X1 @ X0 ) @ X2 ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( ( syntax_ac_operator_a @ f )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f45,plain,
! [X2: a,X0: a,X1: a] :
( ( f @ X1 @ ( f @ X0 @ X2 ) )
= ( f @ ( f @ X1 @ X0 ) @ X2 ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f51,plain,
( syntax_ac_operator_a
= ( ^ [Y0: a > a > a] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f53,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f57,plain,
( $true
= ( ^ [Y0: a > a > a] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y1 @ Y2 )
= ( Y0 @ Y2 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y1 @ ( Y0 @ Y3 @ Y2 ) )
= ( Y0 @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) ) )
@ f ) ),
inference(definition_unfolding,[],[f44,f51]) ).
thf(f114,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y0 @ Y1 )
= ( f @ Y1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( f @ Y0 @ ( f @ Y2 @ Y1 ) )
= ( f @ ( f @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f116,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y0 @ Y1 )
= ( f @ Y1 @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f117,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y0 @ Y1 )
= ( f @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( f @ X1 @ Y0 )
= ( f @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f117]) ).
thf(f119,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( f @ X1 @ Y0 )
= ( f @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X2: a,X1: a] :
( ( ( f @ X1 @ X2 )
= ( f @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X2: a,X1: a] :
( ( f @ X1 @ X2 )
= ( f @ X2 @ X1 ) ),
inference(equality_proxy_clausification,[],[f120]) ).
thf(f141,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ c @ b ) ) ),
inference(forward_demodulation,[],[f53,f45]) ).
thf(f142,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ b @ c ) ) ),
inference(forward_demodulation,[],[f141,f121]) ).
thf(f143,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % 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 20:08:53 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 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
% 0.22/0.30 % (837105)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (837115)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=697748091:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (837115) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-837105-837115"...
% 0.22/0.30 % (837116)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (837116)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
% 0.22/0.30 % (837115)...printing done.
% 0.22/0.30 % (837115)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (837115)------------------------------
% 0.22/0.30 % (837115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (837115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (837115)CaDiCaL version: 2.1.3
% 0.22/0.30 % (837115)Termination reason: Refutation
% 0.22/0.30 % (837115)Time elapsed: 0.004 s
% 0.22/0.30 % (837115)Peak memory usage: 12 MB
% 0.22/0.30 % (837115)Instructions burned: 12 (million)
% 0.22/0.30 % (837105)Success in time 0.035 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------