%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP209^3 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 120 ( 8 ~; 0 |; 0 &; 112 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 4 con; 0-4 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 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_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[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,
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(f2,axiom,
! [X1: a,X0: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).
thf(f3,axiom,
! [X2: a,X0: a,X1: a] :
( ( f @ X0 @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(f11,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox/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(f27,plain,
! [X1: a,X0: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
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 @ X2 @ ( f @ X1 @ X0 ) )
= ( f @ X1 @ ( f @ X2 @ X0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
! [X0: a,X1: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
inference(rectify,[],[f27]) ).
thf(f45,plain,
! [X2: a,X0: a,X1: a] :
( ( f @ X2 @ ( f @ X1 @ X0 ) )
= ( f @ X1 @ ( f @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f50,plain,
! [X0: a,X1: a] :
( ( f @ X0 @ X1 )
= ( f @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f53,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f57,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ b @ ( f @ a2 @ c ) ) ),
inference(superposition,[],[f53,f50]) ).
thf(f59,plain,
( ( f @ b @ ( f @ a2 @ c ) )
!= ( f @ c @ ( f @ a2 @ b ) ) ),
inference(forward_demodulation,[],[f57,f50]) ).
thf(f61,plain,
( ( f @ c @ ( f @ b @ a2 ) )
!= ( f @ b @ ( f @ a2 @ c ) ) ),
inference(forward_demodulation,[],[f59,f50]) ).
thf(f93,plain,
( ( f @ b @ ( f @ a2 @ c ) )
!= ( f @ b @ ( f @ c @ a2 ) ) ),
inference(superposition,[],[f61,f45]) ).
thf(f105,plain,
( ( f @ b @ ( f @ a2 @ c ) )
!= ( f @ b @ ( f @ a2 @ c ) ) ),
inference(forward_demodulation,[],[f93,f50]) ).
thf(f106,plain,
$false,
inference(trivial_inequality_removal,[],[f105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP209^3 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.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
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 20:13:57 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.29 % (1289425)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1289431)lrs+10_16_si=on:nwc=1.5:random_seed=2472927082:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (1289432)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=225339642:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (1289434)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2786918391:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (1289430)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2089295212:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (1289433)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=1153126216: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)
% 0.22/0.29 % (1289432)Instruction limit reached!
% 0.22/0.29 % (1289432)------------------------------
% 0.22/0.29 % (1289432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1289432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1289432)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1289432)Termination reason: Instruction limit
% 0.22/0.29 % (1289432)Termination phase: Saturation
% 0.22/0.29 % (1289432)Time elapsed: 0.002 s
% 0.22/0.29 % (1289432)Peak memory usage: 11 MB
% 0.22/0.29 % (1289432)Instructions burned: 4 (million)
% 0.22/0.29 % (1289434) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1289425-1289434"...
% 0.22/0.29 % (1289431) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1289425-1289431"...
% 0.22/0.29 % (1289430) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1289425-1289430"...
% 0.22/0.29 % (1289434)...printing done.
% 0.22/0.29 % (1289434)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (1289434)------------------------------
% 0.22/0.29 % (1289434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1289434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1289434)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1289434)Termination reason: Refutation
% 0.22/0.29 % (1289434)Time elapsed: 0.005 s
% 0.22/0.29 % (1289434)Peak memory usage: 12 MB
% 0.22/0.29 % (1289434)Instructions burned: 8 (million)
% 0.22/0.29 % (1289425)Success in time 0.038 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------