%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM742^1 : 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 : n013.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 08:19:25 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 20 unt; 0 typ; 2 def)
% Number of atoms : 292 ( 79 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 331 ( 56 ~; 47 |; 0 &; 204 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 66 :)
% 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,
lessf: frac > frac > $o ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
lessf @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( lessf @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45) ).
thf(f5,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(f6,axiom,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).
thf(f7,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(f8,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).
thf(f9,negated_conjecture,
~ ( lessf @ x @ z ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f11,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
lessf @ y @ z,
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( lessf @ y @ z )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( lessf @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( ( eq @ X1 @ X3 )
= $true )
=> ( ( lessf @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f19,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ X0 @ X2 ) ) ),
inference(rectify,[],[f6]) ).
thf(f21,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( lessf @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[],[f7]) ).
thf(f23,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
~ ( lessf @ x @ z ),
inference(rectify,[],[f9]) ).
thf(f25,plain,
( ( lessf @ x @ z )
!= $true ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f11]) ).
thf(f28,plain,
( ( lessf @ x @ z )
!= $true ),
inference(flattening,[],[f25]) ).
thf(f29,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( lessf @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( lessf @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X3 )
!= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f31]) ).
thf(f33,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f34]) ).
thf(f36,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f37,plain,
( ( lessf @ y @ z )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f39,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ X1 @ X3 )
!= $true )
| ( ( lessf @ X2 @ X3 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X2 )
= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f42,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f43,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f48,definition,
( spl0_1
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f50,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f52,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f54,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f55,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f36,f52,f48]) ).
thf(f69,plain,
( ( $true != $true )
| ( $true
= ( eq @ y @ x ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f40,f54]) ).
thf(f70,plain,
( ( $true
= ( eq @ y @ x ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f73,plain,
! [X0: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ X0 @ z ) )
| ( $true
!= ( lessf @ X0 @ y ) ) ),
inference(constrained_superposition,[],[f41,f37]) ).
thf(f75,plain,
! [X0: frac] :
( ( $true
!= ( lessf @ X0 @ y ) )
| ( $true
= ( lessf @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f78,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
!= ( lessf @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f39,f42]) ).
thf(f81,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
= ( lessf @ X1 @ X0 ) )
| ( $true
!= ( lessf @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f119,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( $true
= ( lessf @ x @ X0 ) )
| ( $true
!= ( lessf @ y @ X0 ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f81,f70]) ).
thf(f120,plain,
( ! [X0: frac] :
( ( $true
!= ( lessf @ y @ X0 ) )
| ( $true
= ( lessf @ x @ X0 ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f156,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f120,f37]) ).
thf(f159,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f162,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f159,f43]) ).
thf(f163,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f162]) ).
thf(f166,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f75,f50]) ).
thf(f167,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f170,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f167,f43]) ).
thf(f171,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f170]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f163]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f171]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f172,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM742^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n013.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 12:47:21 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.28 Running first-order model finding
% 0.25/0.28 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
% 0.25/0.32 % (2053171)Will run a generic schedule for satisfiability detection.
% 0.25/0.32 % (2053177)% WARNING: option uhcvi not known.
% 0.25/0.32 % (2053177)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4226867839:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.25/0.32 % (2053177)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.32 % (2053177)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.25/0.32 % (2053176)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4201588993_3000 on theBenchmark for (3000ds/0Mi)
% 0.25/0.32 % Exception at run slice level
% 0.25/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.32 % (2053177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2053171-2053177"...
% 0.25/0.32 % (2053177)...printing done.
% 0.25/0.32 % (2053177)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.32 % (2053177)------------------------------
% 0.25/0.32 % (2053177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.32 % (2053177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.32 % (2053177)CaDiCaL version: 2.1.3
% 0.25/0.32 % (2053177)Termination reason: Refutation
% 0.25/0.32 % (2053177)Time elapsed: 0.007 s
% 0.25/0.32 % (2053177)Peak memory usage: 13 MB
% 0.25/0.32 % (2053177)Instructions burned: 12 (million)
% 0.25/0.32 % (2053171)Success in time 0.029 s
% 0.25/0.32 % Vampire exiting
%------------------------------------------------------------------------------