%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYP119^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:50:41 AM UTC 2026
% Result : Theorem 0.10s 0.16s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 178 ( 16 ~; 5 |; 3 &; 154 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 42 ( 0 ^; 39 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
i:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
o:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
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,
sK2: sK1 > sK0 ).
thf(func_def_6,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_9,type,
sK4: sK1 ).
thf(func_def_10,type,
sK5: sK1 ).
thf(f1,axiom,
! [X0: $tType,X3: X0] :
( ( i @ X0 @ X3 )
= X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/I_THM_') ).
thf(f3,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X5: X2,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 )
= ( X3 @ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/o_THM_') ).
thf(f5,conjecture,
! [X1: $tType,X0: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
= X2 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/I_O_ID_') ).
thf(f6,negated_conjecture,
~ ! [X1: $tType,X0: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
= X2 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f10,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
~ ! [X1: $tType,X0: $tType,X2: X1 > X0] :
( ( ( o @ X1 @ X1 @ X0 @ X2 @ i @ X1 )
= X2 )
& ( ( o @ X0 @ X1 @ X0 @ i @ X0 @ X2 )
= X2 ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
! [X1: $tType,X2: $tType,X0: $tType,X3: X1,X5: X1 > X2,X4: X2 > X0] :
( ( o @ X2 @ X1 @ X0 @ X4 @ X5 @ X3 )
= ( X4 @ ( X5 @ X3 ) ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
? [X0: $tType,X1: $tType,X2: X1 > X0] :
( ( ( o @ X1 @ X1 @ X0 @ X2 @ i @ X1 )
!= X2 )
| ( ( o @ X0 @ X1 @ X0 @ i @ X0 @ X2 )
!= X2 ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X0 > X1,X5: X1 > X2] :
( ( X5 @ ( X4 @ X3 ) )
= ( o @ X1 @ X0 @ X2 @ X5 @ X4 @ X3 ) ),
inference(rectify,[],[f12]) ).
thf(f16,plain,
( ( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 )
!= sK2 )
| ( ( o @ sK0 @ sK1 @ sK0 @ i @ sK0 @ sK2 )
!= sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f20,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(cnf_transformation,[],[f10]) ).
thf(f21,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X0 > X1,X5: X1 > X2] :
( ( X5 @ ( X4 @ X3 ) )
= ( o @ X1 @ X0 @ X2 @ X5 @ X4 @ X3 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( ( ( o @ sK0 @ sK1 @ sK0 @ i @ sK0 @ sK2 )
!= sK2 )
| ( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 )
!= sK2 ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f27,plain,
( ( ( o @ sK0 @ sK1 @ sK0 @ i @ sK0 @ sK2 @ sK4 )
!= ( sK2 @ sK4 ) )
| ( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 )
!= sK2 ) ),
inference(negative_extensionality,[],[f23]) ).
thf(f31,plain,
( ( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 )
!= sK2 )
| ( ( i @ sK0 @ ( sK2 @ sK4 ) )
!= ( sK2 @ sK4 ) ) ),
inference(superposition,[],[f27,f21]) ).
thf(f32,plain,
( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 )
!= sK2 ),
inference(forward_subsumption_resolution,[],[f31,f20]) ).
thf(f33,plain,
( ( o @ sK1 @ sK1 @ sK0 @ sK2 @ i @ sK1 @ sK5 )
!= ( sK2 @ sK5 ) ),
inference(negative_extensionality,[],[f32]) ).
thf(f34,plain,
( ( sK2 @ ( i @ sK1 @ sK5 ) )
!= ( sK2 @ sK5 ) ),
inference(forward_demodulation,[],[f33,f21]) ).
thf(f35,plain,
( ( sK2 @ sK5 )
!= ( sK2 @ sK5 ) ),
inference(forward_demodulation,[],[f34,f20]) ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYP119^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:28:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.13 Running higher-order theorem proving
% 0.10/0.14 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
% 0.10/0.16 % (422605)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.16 % (422616)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.16 % (422616)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
% 0.10/0.16 % (422610)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1920153330:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.10/0.16 % (422612)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3474108784:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.10/0.16 % (422611)lrs+10_16_si=on:nwc=1.5:random_seed=904272821:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.10/0.16 % (422614)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1281816902:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.10/0.16 % (422615)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3794844712:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.10/0.16 % (422613)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=4172288438: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_3000 on theBenchmark for (3000ds/634Mi)
% 0.10/0.16 % (422616)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=374489820:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.10/0.16 % (422610) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-422605-422610"...
% 0.10/0.16 % (422612) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-422605-422612"...
% 0.10/0.16 % (422614) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-422605-422614"...
% 0.10/0.16 % (422611) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-422605-422611"...
% 0.10/0.16 % (422614)...printing done.
% 0.10/0.16 % (422612)...printing done.
% 0.10/0.16 % (422610)...printing done.
% 0.10/0.16 % (422611)...printing done.
% 0.10/0.16 % (422614)Refutation found. Thanks to Tanya!
% 0.10/0.16 % SZS status Theorem for theBenchmark
% 0.10/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.16 % (422614)------------------------------
% 0.10/0.16 % (422614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.16 % (422614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.16 % (422614)CaDiCaL version: 2.1.3
% 0.10/0.16 % (422614)Termination reason: Refutation
% 0.10/0.16 % (422614)Time elapsed: 0.001 s
% 0.10/0.16 % (422614)Peak memory usage: 12 MB
% 0.10/0.16 % (422614)Instructions burned: 3 (million)
% 0.10/0.16 % (422605)Success in time 0.015 s
% 0.10/0.16 % Vampire exiting
%------------------------------------------------------------------------------