%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM767^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:19:29 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 240 ( 23 ~; 17 |; 0 &; 188 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% 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,
v: frac ).
thf(func_def_3,type,
w: frac ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_5,type,
pf: frac > frac > frac ).
thf(f1,axiom,
eq @ ( pf @ y @ v ) @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(f2,axiom,
eq @ ( pf @ y @ w ) @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(f3,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
=> ( eq @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63e) ).
thf(f4,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(f5,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(f6,conjecture,
eq @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz67b) ).
thf(f7,negated_conjecture,
~ ( eq @ v @ w ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
eq @ ( pf @ y @ v ) @ x,
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
eq @ ( pf @ y @ w ) @ x,
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( eq @ ( pf @ y @ w ) @ x )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
~ ( eq @ v @ w ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
( ( eq @ v @ w )
!= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( eq @ v @ w )
!= $true ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f22,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f23,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f25,plain,
( ( eq @ ( pf @ y @ v ) @ x )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
( ( eq @ ( pf @ y @ w ) @ x )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f27,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X2 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f30,plain,
( ( eq @ v @ w )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f47,plain,
( ( $true != $true )
| ( $true
= ( eq @ x @ ( pf @ y @ v ) ) ) ),
inference(constrained_superposition,[],[f29,f25]) ).
thf(f50,plain,
( $true
= ( eq @ x @ ( pf @ y @ v ) ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f79,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
= ( eq @ X0 @ ( pf @ y @ v ) ) )
| ( $true
!= ( eq @ X0 @ x ) ) ),
inference(constrained_superposition,[],[f28,f50]) ).
thf(f85,plain,
! [X0: frac] :
( ( $true
!= ( eq @ X0 @ x ) )
| ( $true
= ( eq @ X0 @ ( pf @ y @ v ) ) ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f109,plain,
( ( $true != $true )
| ( $true
= ( eq @ ( pf @ y @ w ) @ ( pf @ y @ v ) ) ) ),
inference(constrained_superposition,[],[f85,f26]) ).
thf(f110,plain,
( $true
= ( eq @ ( pf @ y @ w ) @ ( pf @ y @ v ) ) ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f118,plain,
( ( $true != $true )
| ( $true
= ( eq @ ( pf @ y @ v ) @ ( pf @ y @ w ) ) ) ),
inference(constrained_superposition,[],[f29,f110]) ).
thf(f121,plain,
( $true
= ( eq @ ( pf @ y @ v ) @ ( pf @ y @ w ) ) ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f139,plain,
( ( $true != $true )
| ( ( eq @ v @ w )
= $true ) ),
inference(constrained_superposition,[],[f27,f121]) ).
thf(f140,plain,
( ( eq @ v @ w )
= $true ),
inference(trivial_inequality_removal,[],[f139]) ).
thf(f158,plain,
$true != $true,
inference(constrained_superposition,[],[f30,f140]) ).
thf(f159,plain,
$false,
inference(trivial_inequality_removal,[],[f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM767^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 12:54:03 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26 % (715102)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (715109)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4238557365_3000 on theBenchmark for (3000ds/0Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (715110)% WARNING: option uhcvi not known.
% 0.10/0.26 % (715110)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=910689840:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.10/0.26 % (715112)dis+10_1_sil=32000:sp=arity:random_seed=3621202737:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.10/0.26 % (715111)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=561079404:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.10/0.26 % (715113)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2567097973:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.10/0.26 % (715110)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (715114)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=619218558:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.10/0.26 % (715110)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.26 % (715116)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1900070718:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.10/0.26 % (715113)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (715122)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3269059433:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (715116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-715102-715116"...
% 0.10/0.26 % (715114) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-715102-715114"...
% 0.10/0.26 % (715116)...printing done.
% 0.10/0.26 % (715112) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-715102-715112"...
% 0.10/0.26 % (715116)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (715116)------------------------------
% 0.10/0.26 % (715116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (715116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (715116)CaDiCaL version: 2.1.3
% 0.10/0.26 % (715116)Termination reason: Refutation
% 0.10/0.26 % (715116)Time elapsed: 0.006 s
% 0.10/0.26 % (715116)Peak memory usage: 12 MB
% 0.10/0.26 % (715116)Instructions burned: 9 (million)
% 0.10/0.26 % (715102)Success in time 0.032 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------