%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM751^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:18:45 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 56 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 309 ( 35 ~; 28 |; 0 &; 234 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
z: frac ).
thf(func_def_3,type,
moref: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(func_def_6,type,
eq: frac > frac > $o ).
thf(f1,axiom,
moref @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(f3,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62a) ).
thf(f4,axiom,
! [X1: frac,X0: frac] : ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(f5,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62d) ).
thf(f6,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X1: frac,X3: frac,X2: frac,X0: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X3 )
= $true )
=> ( ( moref @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: frac,X1: frac] : ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
! [X1: frac,X0: frac] :
( $true
= ( eq @ ( pf @ X1 @ X0 ) @ ( pf @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X0 @ X2 )
=> ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X2: frac,X1: frac,X0: frac] :
( ( $true
= ( moref @ X0 @ X2 ) )
=> ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
moref @ x @ y,
inference(rectify,[],[f1]) ).
thf(f14,plain,
( ( moref @ x @ y )
= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
!= ( moref @ X0 @ X2 ) )
| ( ( moref @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f19,plain,
! [X1: frac,X3: frac,X2: frac,X0: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( moref @ X2 @ X3 )
= $true ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(rectify,[],[f10]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true ) ),
inference(rectify,[],[f18]) ).
thf(f23,plain,
( ( moref @ x @ y )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
! [X0: frac,X1: frac] :
( ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X1 @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X1 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f26,plain,
( ( moref @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) )
= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac,X4: frac] :
( ( $true
!= ( moref @ X0 @ X2 ) )
| ( ( moref @ X3 @ X4 )
= $true )
| ( ( eq @ ( pf @ X0 @ X1 ) @ X3 )
!= $true )
| ( ( eq @ ( pf @ X2 @ X1 ) @ X4 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f25,f27]) ).
thf(f31,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac,X4: frac] :
( ( ( eq @ ( pf @ X2 @ X1 ) @ X4 )
!= $true )
| ( ( moref @ X3 @ X4 )
= $true )
| ( ( eq @ ( pf @ X0 @ X1 ) @ X3 )
!= $true )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f33,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( ( moref @ X2 @ ( pf @ X1 @ X0 ) )
= $true )
| ( ( moref @ X3 @ X0 )
!= $true )
| ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
!= $true ) ),
inference(superposition,[],[f31,f24]) ).
thf(f34,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X3 @ X1 ) @ X2 )
!= $true )
| ( ( moref @ X2 @ ( pf @ X1 @ X0 ) )
= $true )
| ( ( moref @ X3 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(superposition,[],[f34,f24]) ).
thf(f36,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) )
| ( $true
!= ( moref @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(superposition,[],[f26,f36]) ).
thf(f39,plain,
( ( moref @ x @ y )
!= $true ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f41,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM751^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:49:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.12 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
% 0.08/0.15 % (61043)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.15 % (61054)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.15 % (61054)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
% 0.08/0.15 % (61050)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2503223387:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.15 % (61049)lrs+10_16_si=on:nwc=1.5:random_seed=126554156:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.15 % (61048)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3604046281:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.15 % (61052)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3886901970:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.15 % (61051)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=3477559101: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)
% 0.08/0.15 % (61053)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1551671072:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.15 % (61054)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=4287031440:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.15 % (61052) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61052"...
% 0.08/0.15 % (61048) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61048"...
% 0.08/0.15 % (61050) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61050"...
% 0.08/0.15 % (61049) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61049"...
% 0.08/0.15 % (61051) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61051"...
% 0.08/0.15 % (61050)...printing done.
% 0.08/0.15 % (61048)...printing done.
% 0.08/0.15 % (61052)...printing done.
% 0.08/0.15 % (61049)...printing done.
% 0.08/0.15 % (61051)...printing done.
% 0.08/0.15 % (61053) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-61043-61053"...
% 0.08/0.15 % (61052)Refutation found. Thanks to Tanya!
% 0.08/0.15 % SZS status Theorem for theBenchmark
% 0.08/0.15 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.15 % (61052)------------------------------
% 0.08/0.15 % (61052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.15 % (61052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.15 % (61052)CaDiCaL version: 2.1.3
% 0.08/0.15 % (61052)Termination reason: Refutation
% 0.08/0.15 % (61052)Time elapsed: 0.002 s
% 0.08/0.15 % (61052)Peak memory usage: 12 MB
% 0.08/0.15 % (61052)Instructions burned: 5 (million)
% 0.08/0.15 % (61043)Success in time 0.023 s
% 0.08/0.15 % Vampire exiting
%------------------------------------------------------------------------------