%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV091^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:37:37 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 465 ( 129 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 489 ( 61 ~; 68 |; 40 &; 304 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 0 ^; 139 !; 12 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cP: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X1 @ X2 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cP @ X0 @ X1 )
| ( cQ @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X0: $i,X2: $i,X1: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) ) )
=> ( ! [X1: $i,X0: $i] : ( cQ @ X0 @ X1 )
| ! [X1: $i,X0: $i] : ( cP @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCADE13_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X1 @ X2 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cP @ X0 @ X1 )
| ( cQ @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X0: $i,X2: $i,X1: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) ) )
=> ( ! [X1: $i,X0: $i] : ( cQ @ X0 @ X1 )
| ! [X1: $i,X0: $i] : ( cP @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X2 @ X0 )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X2 @ X1 ) )
& ! [X3: $i,X4: $i] :
( ( cP @ X4 @ X3 )
| ( cQ @ X4 @ X3 ) )
& ! [X5: $i,X6: $i] :
( ( cQ @ X5 @ X6 )
=> ( cQ @ X6 @ X5 ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( cQ @ X9 @ X8 )
& ( cQ @ X7 @ X9 ) )
=> ( cQ @ X7 @ X8 ) ) )
=> ( ! [X10: $i,X11: $i] : ( cQ @ X11 @ X10 )
| ! [X12: $i,X13: $i] : ( cP @ X13 @ X12 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X9: $i,X7: $i,X8: $i] :
( ( ( ( cQ @ X7 @ X9 )
= $true )
& ( ( cQ @ X9 @ X8 )
= $true ) )
=> ( ( cQ @ X7 @ X8 )
= $true ) )
& ! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
= $true )
| ( ( cQ @ X4 @ X3 )
= $true ) )
& ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( cP @ X2 @ X0 )
= $true )
& ( ( cP @ X0 @ X1 )
= $true ) )
=> ( $true
= ( cP @ X2 @ X1 ) ) )
& ! [X5: $i,X6: $i] :
( ( ( cQ @ X5 @ X6 )
= $true )
=> ( ( cQ @ X6 @ X5 )
= $true ) ) )
=> ( ! [X10: $i,X11: $i] :
( $true
= ( cQ @ X11 @ X10 ) )
| ! [X12: $i,X13: $i] :
( ( cP @ X13 @ X12 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X11: $i,X10: $i] :
( $true
!= ( cQ @ X11 @ X10 ) )
& ? [X12: $i,X13: $i] :
( ( cP @ X13 @ X12 )
!= $true )
& ! [X9: $i,X7: $i,X8: $i] :
( ( ( cQ @ X7 @ X8 )
= $true )
| ( ( cQ @ X7 @ X9 )
!= $true )
| ( ( cQ @ X9 @ X8 )
!= $true ) )
& ! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
= $true )
| ( ( cQ @ X4 @ X3 )
= $true ) )
& ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( cP @ X2 @ X1 ) )
| ( ( cP @ X2 @ X0 )
!= $true )
| ( ( cP @ X0 @ X1 )
!= $true ) )
& ! [X6: $i,X5: $i] :
( ( ( cQ @ X6 @ X5 )
= $true )
| ( ( cQ @ X5 @ X6 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X12: $i,X13: $i] :
( ( cP @ X13 @ X12 )
!= $true )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cP @ X0 @ X1 )
!= $true )
| ( $true
= ( cP @ X2 @ X1 ) )
| ( ( cP @ X2 @ X0 )
!= $true ) )
& ? [X11: $i,X10: $i] :
( $true
!= ( cQ @ X11 @ X10 ) )
& ! [X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
= $true )
| ( ( cQ @ X4 @ X3 )
= $true ) )
& ! [X8: $i,X9: $i,X7: $i] :
( ( ( cQ @ X9 @ X8 )
!= $true )
| ( ( cQ @ X7 @ X8 )
= $true )
| ( ( cQ @ X7 @ X9 )
!= $true ) )
& ! [X6: $i,X5: $i] :
( ( ( cQ @ X6 @ X5 )
= $true )
| ( ( cQ @ X5 @ X6 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ( cP @ X1 @ X0 )
!= $true )
& ! [X2: $i,X3: $i,X4: $i] :
( ( $true
!= ( cP @ X3 @ X2 ) )
| ( ( cP @ X4 @ X2 )
= $true )
| ( ( cP @ X4 @ X3 )
!= $true ) )
& ? [X5: $i,X6: $i] :
( ( cQ @ X5 @ X6 )
!= $true )
& ! [X7: $i,X8: $i] :
( ( ( cP @ X8 @ X7 )
= $true )
| ( ( cQ @ X8 @ X7 )
= $true ) )
& ! [X9: $i,X10: $i,X11: $i] :
( ( $true
!= ( cQ @ X10 @ X9 ) )
| ( ( cQ @ X11 @ X9 )
= $true )
| ( $true
!= ( cQ @ X11 @ X10 ) ) )
& ! [X12: $i,X13: $i] :
( ( ( cQ @ X12 @ X13 )
= $true )
| ( ( cQ @ X13 @ X12 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cP @ sK1 @ sK0 )
!= $true )
& ! [X2: $i,X3: $i,X4: $i] :
( ( $true
!= ( cP @ X3 @ X2 ) )
| ( ( cP @ X4 @ X2 )
= $true )
| ( ( cP @ X4 @ X3 )
!= $true ) )
& ( $true
!= ( cQ @ sK2 @ sK3 ) )
& ! [X7: $i,X8: $i] :
( ( ( cP @ X8 @ X7 )
= $true )
| ( ( cQ @ X8 @ X7 )
= $true ) )
& ! [X9: $i,X10: $i,X11: $i] :
( ( $true
!= ( cQ @ X10 @ X9 ) )
| ( ( cQ @ X11 @ X9 )
= $true )
| ( $true
!= ( cQ @ X11 @ X10 ) ) )
& ! [X12: $i,X13: $i] :
( ( ( cQ @ X12 @ X13 )
= $true )
| ( ( cQ @ X13 @ X12 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f7]) ).
thf(f9,plain,
! [X12: $i,X13: $i] :
( ( ( cQ @ X13 @ X12 )
!= $true )
| ( ( cQ @ X12 @ X13 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X10: $i,X11: $i,X9: $i] :
( ( $true
!= ( cQ @ X11 @ X10 ) )
| ( $true
!= ( cQ @ X10 @ X9 ) )
| ( ( cQ @ X11 @ X9 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X8: $i,X7: $i] :
( ( ( cP @ X8 @ X7 )
= $true )
| ( ( cQ @ X8 @ X7 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( cQ @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( ( cP @ X4 @ X3 )
!= $true )
| ( $true
!= ( cP @ X3 @ X2 ) )
| ( ( cP @ X4 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( cP @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( ( ( cQ @ sK1 @ sK0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f14,f11]) ).
thf(f17,plain,
( ( cQ @ sK1 @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
( ( ( cQ @ sK0 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f9,f17]) ).
thf(f19,plain,
( ( cQ @ sK0 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f18]) ).
thf(f22,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ sK1 @ X0 )
= $true )
| ( ( cQ @ sK0 @ X0 )
!= $true ) ),
inference(superposition,[],[f10,f17]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( cQ @ sK1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( cQ @ sK0 @ X0 )
= $true ) ),
inference(superposition,[],[f10,f19]) ).
thf(f24,plain,
! [X0: $i] :
( ( ( cQ @ sK0 @ X0 )
= $true )
| ( ( cQ @ sK1 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
! [X0: $i] :
( ( ( cQ @ sK0 @ X0 )
!= $true )
| ( ( cQ @ sK1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f31,plain,
! [X0: $i] :
( ( ( cQ @ X0 @ sK0 )
= $true )
| ( $true != $true )
| ( ( cQ @ sK1 @ X0 )
!= $true ) ),
inference(superposition,[],[f9,f24]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( cQ @ sK1 @ X0 )
!= $true )
| ( ( cQ @ X0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f34,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( ( cP @ X0 @ X2 )
= $true )
| ( ( cP @ X1 @ X2 )
!= $true ) ),
inference(superposition,[],[f13,f11]) ).
thf(f35,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X1 @ X2 )
!= $true )
| ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cP @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cQ @ X2 @ X0 )
= $true )
| ( ( cQ @ X0 @ X1 )
= $true )
| ( $true
= ( cP @ X2 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[],[f35,f11]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cP @ X2 @ X1 ) )
| ( ( cQ @ X2 @ X0 )
= $true )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f45,plain,
! [X0: $i] :
( ( ( cQ @ sK1 @ X0 )
= $true )
| ( $true != $true )
| ( ( cQ @ X0 @ sK0 )
= $true ) ),
inference(superposition,[],[f14,f44]) ).
thf(f55,plain,
! [X0: $i] :
( ( ( cQ @ sK1 @ X0 )
= $true )
| ( ( cQ @ X0 @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f63,plain,
! [X0: $i] :
( ( cQ @ X0 @ sK0 )
= $true ),
inference(forward_subsumption_resolution,[],[f55,f33]) ).
thf(f65,plain,
! [X0: $i] :
( ( ( cQ @ sK0 @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f9,f63]) ).
thf(f70,plain,
! [X0: $i] :
( ( cQ @ sK0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f72,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ sK1 @ X0 )
= $true ) ),
inference(superposition,[],[f25,f70]) ).
thf(f75,plain,
! [X0: $i] :
( ( cQ @ sK1 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f80,plain,
! [X0: $i] :
( ( ( cQ @ X0 @ sK1 )
= $true )
| ( $true != $true ) ),
inference(superposition,[],[f9,f75]) ).
thf(f82,plain,
! [X0: $i] :
( ( cQ @ X0 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f84,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cQ @ sK1 @ X1 )
!= $true )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(superposition,[],[f10,f82]) ).
thf(f91,plain,
! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cQ @ sK1 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f92,plain,
! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
= $true ),
inference(forward_subsumption_resolution,[],[f91,f75]) ).
thf(f97,plain,
$true != $true,
inference(superposition,[],[f12,f92]) ).
thf(f98,plain,
$false,
inference(trivial_inequality_removal,[],[f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV091^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n004.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:09:39 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running higher-order theorem proving
% 0.26/0.29 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
% 0.26/0.33 % (1408119)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.33 % (1408127)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=1205408077: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)
% 0.26/0.33 % (1408128)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2632096863:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.33 % (1408130)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.33 % (1408128) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1408119-1408128"...
% 0.26/0.33 % (1408130)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
% 0.26/0.33 % (1408128)...printing done.
% 0.26/0.33 % (1408128)Refutation found. Thanks to Tanya!
% 0.26/0.33 % SZS status Theorem for theBenchmark
% 0.26/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.34 % (1408128)------------------------------
% 0.26/0.34 % (1408128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (1408128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (1408128)CaDiCaL version: 2.1.3
% 0.26/0.34 % (1408128)Termination reason: Refutation
% 0.26/0.34 % (1408128)Time elapsed: 0.007 s
% 0.26/0.34 % (1408128)Peak memory usage: 12 MB
% 0.26/0.34 % (1408128)Instructions burned: 10 (million)
% 0.26/0.34 % (1408119)Success in time 0.033 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------