%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM771^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:18:50 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 54 ( 45 unt; 0 typ; 13 def)
% Number of atoms : 91 ( 41 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 219 ( 14 ~; 7 |; 0 &; 196 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 17 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
eq: frac > frac > $o ).
thf(func_def_3,type,
fr: nat > nat > frac ).
thf(func_def_4,type,
ts: nat > nat > nat ).
thf(func_def_5,type,
num: frac > nat ).
thf(func_def_6,type,
den: frac > nat ).
thf(func_def_10,type,
sF0: nat ).
thf(func_def_11,type,
sF1: nat ).
thf(func_def_12,type,
sF2: nat ).
thf(func_def_13,type,
sF3: nat ).
thf(func_def_14,type,
sF4: nat ).
thf(func_def_15,type,
sF5: nat ).
thf(func_def_16,type,
sF6: frac ).
thf(func_def_17,type,
sF7: nat ).
thf(func_def_18,type,
sF8: nat ).
thf(func_def_19,type,
sF9: frac ).
thf(func_def_20,type,
sF10: $o ).
thf(f1,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(f3,conjecture,
eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz69) ).
thf(f4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f12,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( sF0
= ( num @ x ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f17,plain,
( ( num @ x )
= sF0 ),
inference(reorient_equations,[],[f16]) ).
thf(f18,definition,
( sF1
= ( num @ y ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f19,plain,
( ( num @ y )
= sF1 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,definition,
( sF2
= ( ts @ sF0 @ sF1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f21,plain,
( ( ts @ sF0 @ sF1 )
= sF2 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,definition,
( sF3
= ( den @ x ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f23,plain,
( ( den @ x )
= sF3 ),
inference(reorient_equations,[],[f22]) ).
thf(f24,definition,
( sF4
= ( den @ y ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f25,plain,
( ( den @ y )
= sF4 ),
inference(reorient_equations,[],[f24]) ).
thf(f26,definition,
( sF5
= ( ts @ sF3 @ sF4 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f27,plain,
( ( ts @ sF3 @ sF4 )
= sF5 ),
inference(reorient_equations,[],[f26]) ).
thf(f28,definition,
( sF6
= ( fr @ sF2 @ sF5 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f29,definition,
( sF7
= ( ts @ sF1 @ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f30,definition,
( sF8
= ( ts @ sF4 @ sF3 ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f31,definition,
( sF9
= ( fr @ sF7 @ sF8 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f32,plain,
( ( fr @ sF7 @ sF8 )
= sF9 ),
inference(reorient_equations,[],[f31]) ).
thf(f33,definition,
( sF10
= ( eq @ sF6 @ sF9 ) ),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
thf(f34,plain,
$true != sF10,
inference(definition_folding,[],[f13,f33,f32,f30,f23,f25,f29,f17,f19,f28,f27,f25,f23,f21,f19,f17]) ).
thf(f35,plain,
( ( $true = sF10 )
| ( ( eq @ sF6 @ sF9 )
= $false ) ),
inference(iff_proxy_clausification,[],[f33]) ).
thf(f47,definition,
( spl11_3
<=> ( ( eq @ sF6 @ sF9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f49,plain,
( ( ( eq @ sF6 @ sF9 )
= $false )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f51,definition,
( spl11_4
<=> ( $true = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f54,plain,
( spl11_3
| spl11_4 ),
inference(avatar_split_clause,[],[f35,f51,f47]) ).
thf(f55,plain,
~ spl11_4,
inference(avatar_split_clause,[],[f34,f51]) ).
thf(f75,plain,
( ( ts @ sF1 @ sF0 )
= sF2 ),
inference(constrained_superposition,[],[f11,f21]) ).
thf(f76,plain,
( ( ts @ sF3 @ sF4 )
= sF8 ),
inference(constrained_superposition,[],[f11,f30]) ).
thf(f83,plain,
sF7 = sF2,
inference(forward_demodulation,[],[f75,f29]) ).
thf(f85,plain,
sF8 = sF5,
inference(forward_demodulation,[],[f76,f27]) ).
thf(f92,plain,
( sF6
= ( fr @ sF2 @ sF8 ) ),
inference(constrained_superposition,[],[f28,f85]) ).
thf(f93,plain,
( ( fr @ sF7 @ sF8 )
= sF6 ),
inference(forward_demodulation,[],[f92,f83]) ).
thf(f94,plain,
sF6 = sF9,
inference(forward_demodulation,[],[f93,f32]) ).
thf(f98,plain,
( ( ( eq @ sF6 @ sF6 )
= $false )
| ~ spl11_3 ),
inference(constrained_superposition,[],[f49,f94]) ).
thf(f102,plain,
( ( $true = $false )
| ~ spl11_3 ),
inference(forward_demodulation,[],[f98,f12]) ).
thf(f103,plain,
( $false
| ~ spl11_3 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f104,plain,
~ spl11_3,
inference(avatar_contradiction_clause,[],[f103]) ).
cnf(s2,plain,
( spl11_3
| spl11_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
~ spl11_4,
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
~ spl11_3,
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s3,s8]) ).
thf(f105,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM771^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n018.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 12:56:57 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.21 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
% 0.11/0.25 % (29662)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.25 % (29673)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.25 % (29673)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
% 0.11/0.25 % (29673)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=2134070664:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.11/0.25 % (29673) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-29662-29673"...
% 0.11/0.25 % (29673)...printing done.
% 0.11/0.25 % (29673)Refutation found. Thanks to Tanya!
% 0.11/0.25 % SZS status Theorem for theBenchmark
% 0.11/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.25 % (29673)------------------------------
% 0.11/0.25 % (29673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.25 % (29673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.25 % (29673)CaDiCaL version: 2.1.3
% 0.11/0.25 % (29673)Termination reason: Refutation
% 0.11/0.25 % (29673)Time elapsed: 0.002 s
% 0.11/0.25 % (29673)Peak memory usage: 13 MB
% 0.11/0.25 % (29673)Instructions burned: 6 (million)
% 0.11/0.25 % (29662)Success in time 0.025 s
% 0.11/0.25 % Vampire exiting
%------------------------------------------------------------------------------