%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA100^1 : 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 : n016.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 07:45:55 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 220 ( 13 ~; 1 |; 0 &; 206 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 74 ( 20 ^; 46 !; 8 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $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/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK1: 'type/realax/real' ).
thf(func_def_6,type,
sK2: sK0 > $o ).
thf(func_def_7,type,
sK3: sK0 > 'type/realax/real' ).
thf(func_def_10,type,
sK4: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X3: X0 > $o,X2: 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ X2 @ ( X1 @ X4 ) ) )
= ( 'const/realax/real_mul' @ X2 @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_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: $tType,X3: X0 > $o,X2: 'type/realax/real',X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_RMUL_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X3: X0 > $o,X2: 'type/realax/real',X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X3 @ X1 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X3
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X1 @ X4 ) @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0 > $o,X3: 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ X3 @ ( X1 @ X4 ) ) )
= ( 'const/realax/real_mul' @ X3 @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X3: 'type/realax/real',X2: X0 > $o,X1: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X3 @ ( 'const/iterate/sum' @ X0 @ X2 @ X1 ) )
= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X3 @ ( X1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: 'type/realax/real',X3: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [X4: X0] : ( 'const/realax/real_mul' @ ( X3 @ X4 ) @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ! [X0: $tType,X2: 'type/realax/real',X1: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ X2 )
= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X3 @ Y0 ) @ X2 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
? [X0: $tType,X2: 'type/realax/real',X1: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X1 @ X3 ) @ X2 )
!= ( 'const/iterate/sum' @ X0 @ X1
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X3 @ Y0 ) @ X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f11,plain,
! [X0: $tType,X1: 'type/realax/real',X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X1 @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
? [X0: $tType,X1: 'type/realax/real',X2: X0 > $o,X3: X0 > 'type/realax/real'] :
( ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) @ X1 )
!= ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ ( X3 @ Y0 ) @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f13,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f12]) ).
thf(f14,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(rectify,[],[f9]) ).
thf(f15,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ X2
@ ^ [Y0: X0] : ( 'const/realax/real_mul' @ X1 @ ( X3 @ Y0 ) ) )
= ( 'const/realax/real_mul' @ X1 @ ( 'const/iterate/sum' @ X0 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 ) )
!= ( 'const/realax/real_mul' @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) @ sK1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( 'const/realax/real_mul' @ X0 @ X1 )
= ( 'const/realax/real_mul' @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
( ( 'const/iterate/sum' @ sK0 @ sK2
@ ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 ) )
!= ( 'const/realax/real_mul' @ sK1 @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) ) ),
inference(forward_demodulation,[],[f16,f17]) ).
thf(f22,plain,
! [X0: 'type/realax/real',X1: sK0 > 'type/realax/real'] :
( ( ( 'const/realax/real_mul' @ X0 @ ( 'const/iterate/sum' @ sK0 @ sK2 @ X1 ) )
!= ( 'const/realax/real_mul' @ sK1 @ ( 'const/iterate/sum' @ sK0 @ sK2 @ sK3 ) ) )
| ( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ X0 @ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f20,f15]) ).
thf(f26,plain,
( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ sK1 @ ( sK3 @ Y0 ) ) )
!= ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 ) ) ),
inference(equality_resolution,[],[f22]) ).
thf(f28,plain,
( ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ ( sK3 @ Y0 ) @ sK1 )
@ sK4 )
!= ( ^ [Y0: sK0] : ( 'const/realax/real_mul' @ sK1 @ ( sK3 @ Y0 ) )
@ sK4 ) ),
inference(negative_extensionality,[],[f26]) ).
thf(f29,plain,
( ( 'const/realax/real_mul' @ sK1 @ ( sK3 @ sK4 ) )
!= ( 'const/realax/real_mul' @ ( sK3 @ sK4 ) @ sK1 ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA100^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:46:20 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.21/0.28 % (682668)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (682676)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=2201470467: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 % (682676)Refutation not found, incomplete strategy
% 0.21/0.28 % (682676)------------------------------
% 0.21/0.28 % (682676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (682676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (682676)CaDiCaL version: 2.1.3
% 0.21/0.28 % (682676)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (682676)Time elapsed: 0.001 s
% 0.21/0.28 % (682676)Peak memory usage: 12 MB
% 0.21/0.28 % (682676)Instructions burned: 2 (million)
% 0.21/0.28 % (682676)------------------------------
% 0.21/0.28 % (682676)------------------------------
% 0.21/0.28 % (682677)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3734152437:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (682673)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1217393024:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (682675)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3191931309:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (682674)lrs+10_16_si=on:nwc=1.5:random_seed=4052055655:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (682677)Refutation not found, incomplete strategy
% 0.21/0.28 % (682677)------------------------------
% 0.21/0.28 % (682677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (682677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (682677)CaDiCaL version: 2.1.3
% 0.21/0.28 % (682677)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (682677)Time elapsed: 0.001 s
% 0.21/0.28 % (682677)Peak memory usage: 12 MB
% 0.21/0.28 % (682677)Instructions burned: 1 (million)
% 0.21/0.28 % (682673)Refutation not found, incomplete strategy
% 0.21/0.28 % (682673)------------------------------
% 0.21/0.28 % (682673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (682675)Refutation not found, incomplete strategy
% 0.21/0.28 % (682675)------------------------------
% 0.21/0.28 % (682675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (682673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (682675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (682673)CaDiCaL version: 2.1.3
% 0.21/0.28 % (682673)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (682673)Time elapsed: 0.002 s
% 0.21/0.28 % (682675)CaDiCaL version: 2.1.3
% 0.21/0.28 % (682673)Peak memory usage: 12 MB
% 0.21/0.28 % (682675)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.28 % (682675)Time elapsed: 0.001 s
% 0.21/0.28 % (682673)Instructions burned: 1 (million)
% 0.21/0.28 % (682675)Peak memory usage: 12 MB
% 0.21/0.28 % (682675)Instructions burned: 1 (million)
% 0.21/0.28 % (682679)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 % (682679)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 % (682677)------------------------------
% 0.21/0.28 % (682677)------------------------------
% 0.21/0.28 % (682675)------------------------------
% 0.21/0.28 % (682675)------------------------------
% 0.21/0.28 % (682673)------------------------------
% 0.21/0.28 % (682673)------------------------------
% 0.21/0.28 % (682674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-682668-682674"...
% 0.21/0.28 % (682678)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2134416330:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (682681)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2449516656:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.28 % (682679)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=3016858284:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (682674)...printing done.
% 0.21/0.28 % (682681)Instruction limit reached!
% 0.21/0.28 % (682681)------------------------------
% 0.21/0.28 % (682681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (682681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (682681)CaDiCaL version: 2.1.3
% 0.21/0.28 % (682681)Termination reason: Instruction limit
% 0.21/0.28 % (682681)Termination phase: Saturation
% 0.21/0.28 % (682681)Time elapsed: 0.001 s
% 0.21/0.28 % (682681)Peak memory usage: 12 MB
% 0.21/0.28 % (682681)Instructions burned: 3 (million)
% 0.21/0.28 % (682674)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
% 0.21/0.29 % (682674)------------------------------
% 0.21/0.29 % (682674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (682674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (682674)CaDiCaL version: 2.1.3
% 0.21/0.29 % (682674)Termination reason: Refutation
% 0.21/0.29 % (682674)Time elapsed: 0.004 s
% 0.21/0.29 % (682674)Peak memory usage: 12 MB
% 0.21/0.29 % (682674)Instructions burned: 4 (million)
% 0.21/0.29 % (682668)Success in time 0.05 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------