%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 07:45:58 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 160 ( 17 ~; 5 |; 3 &; 128 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 59 ( 22 ^; 33 !; 4 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/realax/real_mul': 'type/realax/real' > 'type/realax/real' > 'type/realax/real' ).
thf(func_def_1,type,
'const/iterate/polynomial_function': ( 'type/realax/real' > 'type/realax/real' ) > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: 'type/realax/real' ).
thf(func_def_8,type,
sK1: 'type/realax/real' > 'type/realax/real' ).
thf(func_def_9,type,
sK2: 'type/realax/real' ).
thf(func_def_10,type,
sK3: 'type/realax/real' > 'type/realax/real' ).
thf(f1,axiom,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_') ).
thf(f2,axiom,
! [X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_MUL_SYM_') ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_RMUL_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
=> ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ Y0 ) ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: 'type/realax/real' > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/polynomial_function' @ X0 )
=> ( 'const/iterate/polynomial_function'
@ ^ [X2: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ X2 ) @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
=> ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ X1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
? [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
= $true )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X0 @ Y0 ) @ X1 ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f11,plain,
! [X1: 'type/realax/real',X0: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X0 )
!= $true )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X1 @ ( X0 @ Y0 ) ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X1 )
= $true )
& ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( X1 @ Y0 ) @ X0 ) )
!= $true ) ),
inference(rectify,[],[f10]) ).
thf(f13,plain,
( ( ( 'const/iterate/polynomial_function' @ sK1 )
= $true )
& ( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
= $true ) ),
inference(rectify,[],[f11]) ).
thf(f15,plain,
( $true
!= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( 'const/iterate/polynomial_function' @ sK1 )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real' > 'type/realax/real'] :
( ( ( 'const/iterate/polynomial_function' @ X1 )
!= $true )
| ( ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
! [X0: 'type/realax/real'] :
( ( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f17,f16]) ).
thf(f27,plain,
! [X0: 'type/realax/real'] :
( $true
= ( 'const/iterate/polynomial_function'
@ ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f28,plain,
! [X0: 'type/realax/real'] :
( ( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f15,f27]) ).
thf(f32,plain,
! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f38,plain,
! [X0: 'type/realax/real'] :
( ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ X0 @ ( sK1 @ Y0 ) )
@ ( sK3 @ X0 ) )
!= ( ^ [Y0: 'type/realax/real'] : ( 'const/realax/real_mul' @ ( sK1 @ Y0 ) @ sK0 )
@ ( sK3 @ X0 ) ) ),
inference(negative_extensionality,[],[f32]) ).
thf(f39,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ ( sK1 @ ( sK3 @ X0 ) ) )
!= ( 'const/realax/real_mul' @ ( sK1 @ ( sK3 @ X0 ) ) @ sK0 ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ sK0 @ ( sK1 @ ( sK3 @ X0 ) ) )
!= ( 'const/realax/real_mul' @ X0 @ ( sK1 @ ( sK3 @ X0 ) ) ) ),
inference(forward_demodulation,[],[f39,f18]) ).
thf(f41,plain,
$false,
inference(equality_resolution,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA125^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:45:31 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.30 % (3489678)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (3489683)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=40156612:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (3489689)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (3489689)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
% 0.21/0.30 % (3489684)lrs+10_16_si=on:nwc=1.5:random_seed=3080876874:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (3489689)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=1687011049:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (3489685)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1290695512:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (3489686)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=3480190585: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)
% 0.21/0.30 % (3489687)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1281180236:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (3489688)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2701651578:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (3489687)Refutation not found, incomplete strategy
% 0.21/0.30 % (3489687)------------------------------
% 0.21/0.30 % (3489687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3489687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3489687)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3489687)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (3489687)Time elapsed: 0.001 s
% 0.21/0.30 % (3489687)Peak memory usage: 12 MB
% 0.21/0.30 % (3489687)Instructions burned: 1 (million)
% 0.21/0.30 % (3489686)Refutation not found, incomplete strategy
% 0.21/0.30 % (3489686)------------------------------
% 0.21/0.30 % (3489686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3489686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3489686)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3489686)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (3489686)Time elapsed: 0.002 s
% 0.21/0.30 % (3489686)Peak memory usage: 12 MB
% 0.21/0.30 % (3489686)Instructions burned: 1 (million)
% 0.21/0.30 % (3489689)Refutation not found, incomplete strategy
% 0.21/0.30 % (3489689)------------------------------
% 0.21/0.30 % (3489689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3489689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3489689)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3489689)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (3489689)Time elapsed: 0.002 s
% 0.21/0.30 % (3489689)Peak memory usage: 12 MB
% 0.21/0.30 % (3489689)Instructions burned: 2 (million)
% 0.21/0.30 % (3489684) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3489678-3489684"...
% 0.21/0.30 % (3489687)------------------------------
% 0.21/0.30 % (3489687)------------------------------
% 0.21/0.30 % (3489686)------------------------------
% 0.21/0.30 % (3489686)------------------------------
% 0.21/0.30 % (3489685)Instruction limit reached!
% 0.21/0.30 % (3489685)------------------------------
% 0.21/0.30 % (3489685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3489685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3489685)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3489685)Termination reason: Instruction limit
% 0.21/0.30 % (3489685)Termination phase: Saturation
% 0.21/0.30 % (3489685)Time elapsed: 0.003 s
% 0.21/0.30 % (3489685)Peak memory usage: 12 MB
% 0.21/0.30 % (3489685)Instructions burned: 4 (million)
% 0.21/0.30 % (3489689)------------------------------
% 0.21/0.30 % (3489689)------------------------------
% 0.21/0.30 % (3489688) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3489678-3489688"...
% 0.21/0.30 % (3489684)...printing done.
% 0.21/0.30 % (3489684)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (3489684)------------------------------
% 0.21/0.30 % (3489684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3489684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3489684)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3489684)Termination reason: Refutation
% 0.21/0.30 % (3489684)Time elapsed: 0.004 s
% 0.21/0.30 % (3489684)Peak memory usage: 12 MB
% 0.21/0.30 % (3489684)Instructions burned: 4 (million)
% 0.21/0.30 % (3489678)Success in time 0.041 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------