%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP209^4 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 55 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 360 ( 5 ~; 0 |; 6 &; 316 @)
% ( 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 : 46 ( 42 usr; 6 con; 0-4 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 89 ( 43 ^; 46 !; 0 ?; 89 :)
% 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:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_1,type,
syntax7388354845996824322omatch:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > $o ) ).
thf(func_def_2,type,
syntax2379306206330768139omatch:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > $o ) ).
thf(func_def_3,type,
a2: a ).
thf(func_def_4,type,
b: a ).
thf(func_def_5,type,
c: a ).
thf(func_def_6,type,
f: a > a > a ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK0:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_19,type,
sK1:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_20,type,
sK2:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_21,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_22,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_23,type,
vNOT: $o > $o ).
thf(func_def_24,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_25,type,
sK6:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_26,type,
sK7:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_27,type,
sK8:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_28,type,
sK9:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_29,type,
sK10:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_30,type,
sK11:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_31,type,
sK12:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_32,type,
sK13:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_33,type,
sK14:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_34,type,
sK15:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_35,type,
sK16:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_36,type,
sK17:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_37,type,
sK18:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_38,type,
sK19:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_39,type,
sK20:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_40,type,
sK21:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_41,type,
sK22:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_42,type,
sK23:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_43,type,
sK24:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(f1,axiom,
syntax_ac_operator @ a @ f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_ac__operator__axioms) ).
thf(f3,axiom,
! [X1: a,X0: a,X2: a] :
( ( f @ X0 @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(f12,axiom,
! [X0: $tType] :
( ( ( ^ [X1: X0 > X0 > X0] :
( ! [X3: X0,X2: X0,X4: X0] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) ) )
= syntax_ac_operator )
@ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ac__operator__def) ).
thf(f13,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f14,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
thf(f21,plain,
! [X0: $tType] :
( ( ( ^ [X1: X0 > X0 > X0] :
( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X3 @ ( X1 @ X2 @ X4 ) )
= ( X1 @ ( X1 @ X3 @ X2 ) @ X4 ) )
& ! [X5: X0,X6: X0] :
( ( X1 @ X5 @ X6 )
= ( X1 @ X6 @ X5 ) ) ) )
= syntax_ac_operator )
@ X0 ),
inference(rectify,[],[f12]) ).
thf(f22,plain,
! [X0: $tType] :
( syntax_ac_operator
@ ( X0
= ( ^ [Y0: X0 > X0 > X0] :
( ( !! @ X0
@ ^ [Y1: X0] :
( !! @ X0
@ ^ [Y2: X0] :
( ( Y0 @ Y2 @ Y1 )
= ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( !! @ X0
@ ^ [Y2: X0] :
( !! @ X0
@ ^ [Y3: X0] :
( ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
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(f33,plain,
! [X0: a,X1: a,X2: a] :
( ( f @ X0 @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ X0 @ X2 ) ) ),
inference(rectify,[],[f3]) ).
thf(f35,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(flattening,[],[f14]) ).
thf(f57,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f58,plain,
! [X0: $tType] :
( syntax_ac_operator
@ ( X0
= ( ^ [Y0: X0 > X0 > X0] :
( ( !! @ X0
@ ^ [Y1: X0] :
( !! @ X0
@ ^ [Y2: X0] :
( ( Y0 @ Y2 @ Y1 )
= ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ X0
@ ^ [Y1: X0] :
( !! @ X0
@ ^ [Y2: X0] :
( !! @ X0
@ ^ [Y3: X0] :
( ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f61,plain,
( ( syntax_ac_operator @ a @ f )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f62,plain,
! [X2: a,X0: a,X1: a] :
( ( f @ X0 @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ X0 @ X2 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f71,plain,
( ( ^ [Y0: a > a > a] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
= ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y1 ) )
= ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
@ f )
= $true ),
inference(definition_unfolding,[],[f61,f58]) ).
thf(f85,plain,
( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y1 @ Y0 )
= ( f @ Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( f @ Y1 @ ( f @ Y2 @ Y0 ) )
= ( f @ ( f @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f86,plain,
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( f @ Y1 @ ( f @ Y2 @ Y0 ) )
= ( f @ ( f @ Y1 @ Y2 ) @ Y0 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y1 @ Y0 )
= ( f @ Y0 @ Y1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f85]) ).
thf(f88,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y1 @ Y0 )
= ( f @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( f @ Y0 @ X1 )
= ( f @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( f @ Y0 @ X1 )
= ( f @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f89]) ).
thf(f91,plain,
! [X2: a,X1: a] :
( ( ( f @ X2 @ X1 )
= ( f @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X2: a,X1: a] :
( ( f @ X1 @ X2 )
= ( f @ X2 @ X1 ) ),
inference(equality_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( f @ Y1 @ ( f @ Y2 @ Y0 ) )
= ( f @ ( f @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f94,plain,
! [X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y0 @ ( f @ Y1 @ X1 ) )
= ( f @ ( f @ Y0 @ Y1 ) @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( f @ Y0 @ ( f @ Y1 @ X1 ) )
= ( f @ ( f @ Y0 @ Y1 ) @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: a,X1: a] :
( ( !! @ a
@ ^ [Y0: a] :
( ( f @ X2 @ ( f @ Y0 @ X1 ) )
= ( f @ ( f @ X2 @ Y0 ) @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
! [X2: a,X3: a,X1: a] :
( ( ^ [Y0: a] :
( ( f @ X2 @ ( f @ Y0 @ X1 ) )
= ( f @ ( f @ X2 @ Y0 ) @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: a,X3: a,X1: a] :
( ( ( f @ X2 @ ( f @ X3 @ X1 ) )
= ( f @ ( f @ X2 @ X3 ) @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f99,plain,
! [X2: a,X3: a,X1: a] :
( ( f @ X2 @ ( f @ X3 @ X1 ) )
= ( f @ ( f @ X2 @ X3 ) @ X1 ) ),
inference(equality_proxy_clausification,[],[f98]) ).
thf(f151,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ b @ ( f @ a2 @ c ) ) ),
inference(forward_demodulation,[],[f57,f92]) ).
thf(f152,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ a2 @ ( f @ b @ c ) ) ),
inference(forward_demodulation,[],[f151,f62]) ).
thf(f153,plain,
$false,
inference(forward_subsumption_resolution,[],[f152,f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209^4 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n001.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:19:51 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 Running higher-order theorem proving
% 0.11/0.26 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
% 0.24/0.33 % (1761748)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.33 % (1761755)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2988377165:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.33 % (1761755)Instruction limit reached!
% 0.24/0.33 % (1761755)------------------------------
% 0.24/0.33 % (1761755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (1761755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (1761755)CaDiCaL version: 2.1.3
% 0.24/0.33 % (1761755)Termination reason: Instruction limit
% 0.24/0.33 % (1761755)Termination phase: Property scanning
% 0.24/0.33 % (1761755)Time elapsed: 0.001 s
% 0.24/0.33 % (1761755)Peak memory usage: 10 MB
% 0.24/0.33 % (1761755)Instructions burned: 4 (million)
% 0.24/0.33 % (1761753)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2817479514:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.33 % (1761756)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=3731434830: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)
% 0.24/0.33 % (1761754)lrs+10_16_si=on:nwc=1.5:random_seed=1192136385:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.33 % (1761753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1761748-1761753"...
% 0.24/0.33 % (1761761)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2949501970:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.33 % (1761754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1761748-1761754"...
% 0.24/0.33 % (1761761)Instruction limit reached!
% 0.24/0.33 % (1761761)------------------------------
% 0.24/0.33 % (1761761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (1761761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (1761761)CaDiCaL version: 2.1.3
% 0.24/0.33 % (1761761)Termination reason: Instruction limit
% 0.24/0.33 % (1761761)Termination phase: Property scanning
% 0.24/0.33 % (1761761)Time elapsed: 0.001 s
% 0.24/0.33 % (1761761)Peak memory usage: 10 MB
% 0.24/0.33 % (1761761)Instructions burned: 4 (million)
% 0.24/0.33 % (1761753)...printing done.
% 0.24/0.33 % (1761756) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1761748-1761756"...
% 0.24/0.33 % (1761754)...printing done.
% 0.24/0.33 % (1761753)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.33 % (1761753)------------------------------
% 0.24/0.33 % (1761753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (1761753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (1761753)CaDiCaL version: 2.1.3
% 0.24/0.33 % (1761753)Termination reason: Refutation
% 0.24/0.33 % (1761753)Time elapsed: 0.007 s
% 0.24/0.33 % (1761753)Peak memory usage: 12 MB
% 0.24/0.33 % (1761753)Instructions burned: 12 (million)
% 0.24/0.33 % (1761748)Success in time 0.052 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------