%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM663^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:19:15 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 138 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 149 ( 30 ~; 21 |; 0 &; 86 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
less: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
less @ y @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X0 @ X1 )
=> ( ( less @ X1 @ X2 )
=> ( less @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz15) ).
thf(f5,conjecture,
less @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(f6,negated_conjecture,
~ ( less @ x @ z ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
less @ y @ z,
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ( less @ y @ z )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( less @ X0 @ X1 )
=> ( ( less @ X1 @ X2 )
=> ( less @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X0 @ X1 )
= $true )
=> ( ( ( less @ X1 @ X2 )
= $true )
=> ( ( less @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( less @ x @ z ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( ( less @ x @ z )
!= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f8]) ).
thf(f19,plain,
( ( less @ x @ z )
!= $true ),
inference(flattening,[],[f16]) ).
thf(f20,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f22,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X1 @ X2 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f23,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X1 @ X2 )
!= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f25,plain,
( ( less @ y @ z )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( less @ X1 @ X2 )
!= $true )
| ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f28,plain,
( ( less @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f33,definition,
( spl0_1
<=> ( ( less @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( less @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl0_2
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f39,plain,
( ( x = y )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f24,f37,f33]) ).
thf(f50,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f25,f39]) ).
thf(f51,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f50,f28]) ).
thf(f52,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f51]) ).
thf(f58,plain,
! [X0: nat] :
( ( $true != $true )
| ( $true
= ( less @ X0 @ z ) )
| ( $true
!= ( less @ X0 @ y ) ) ),
inference(constrained_superposition,[],[f27,f25]) ).
thf(f61,plain,
! [X0: nat] :
( ( $true
!= ( less @ X0 @ y ) )
| ( $true
= ( less @ X0 @ z ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f66,plain,
( ( $true != $true )
| ( ( less @ x @ z )
= $true )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f61,f35]) ).
thf(f67,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f69,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f67,f28]) ).
thf(f70,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f69]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f70]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f71,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM663^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:35:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (534015)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (534021)% WARNING: option uhcvi not known.
% 0.20/0.27 % (534020)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1349711110_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (534022)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1034642477:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (534021)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3129698995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % Exception at run slice level
% 0.20/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.27 % (534021)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (534021)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (534023)dis+10_1_sil=32000:sp=arity:random_seed=1947419863:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (534025)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1017658533:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (534021) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534015-534021"...
% 0.20/0.27 % (534024)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=776071666:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (534023) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534015-534023"...
% 0.20/0.27 % (534024)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (534022) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534015-534022"...
% 0.20/0.27 % (534021)...printing done.
% 0.20/0.27 % (534024) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534015-534024"...
% 0.20/0.27 % (534023)...printing done.
% 0.20/0.27 % (534021)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (534021)------------------------------
% 0.20/0.27 % (534021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (534021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (534021)CaDiCaL version: 2.1.3
% 0.20/0.27 % (534021)Termination reason: Refutation
% 0.20/0.27 % (534021)Time elapsed: 0.003 s
% 0.20/0.27 % (534021)Peak memory usage: 13 MB
% 0.20/0.27 % (534021)Instructions burned: 3 (million)
% 0.20/0.27 % (534015)Success in time 0.039 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------