%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET747^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:23:49 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 236 ( 57 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 415 ( 9 ~; 4 |; 10 &; 336 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 5 con; 0-4 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 108 ( 66 ^; 36 !; 6 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_2,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
fun_injective: ( $i > $i ) > $o ).
thf(func_def_5,type,
fun_surjective: ( $i > $i ) > $o ).
thf(func_def_6,type,
fun_bijective: ( $i > $i ) > $o ).
thf(func_def_7,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
sK0: $i > $i ).
thf(func_def_22,type,
sK1: $i > $i ).
thf(func_def_23,type,
sK2: $i > $i > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f2,axiom,
( fun_composition
= ( ^ [X0: $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_composition) ).
thf(f7,axiom,
( fun_decreasing
= ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X3 ) @ ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_decreasing) ).
thf(f8,axiom,
( fun_increasing
= ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X2 ) @ ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_increasing) ).
thf(f9,conjecture,
! [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( fun_decreasing @ X1 @ X2 )
& ( fun_increasing @ X0 @ X2 ) )
=> ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f10,negated_conjecture,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( fun_decreasing @ X1 @ X2 )
& ( fun_increasing @ X0 @ X2 ) )
=> ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f13,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f20,plain,
( fun_decreasing
= ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X3 ) @ ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f21,plain,
( fun_decreasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( fun_increasing
= ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X2 ) @ ( X0 @ X3 ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f23,plain,
( fun_increasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( fun_decreasing @ X1 @ X2 )
& ( fun_increasing @ X0 @ X2 ) )
=> ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f25,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( ( fun_decreasing @ X1 @ X2 )
= $true )
& ( ( fun_increasing @ X0 @ X2 )
= $true ) )
=> ( ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
? [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( fun_decreasing @ X1 @ X2 )
= $true )
& ( ( fun_increasing @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f27,plain,
? [X0: $i > $i,X1: $i > $i,X2: $i > $i > $o] :
( ( ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( fun_decreasing @ X1 @ X2 )
= $true )
& ( ( fun_increasing @ X0 @ X2 )
= $true ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ( $true
!= ( fun_decreasing @ ( fun_composition @ sK0 @ sK1 ) @ sK2 ) )
& ( $true
= ( fun_decreasing @ sK1 @ sK2 ) )
& ( $true
= ( fun_increasing @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f27]) ).
thf(f30,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f35,plain,
( fun_decreasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f36,plain,
( fun_increasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f37,plain,
( $true
= ( fun_increasing @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f38,plain,
( $true
= ( fun_decreasing @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f39,plain,
( $true
!= ( fun_decreasing @ ( fun_composition @ sK0 @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f43,plain,
( $true
!= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ sK0
@ sK1 )
@ sK2 ) ),
inference(definition_unfolding,[],[f39,f35,f30]) ).
thf(f44,plain,
( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[],[f38,f35]) ).
thf(f45,plain,
( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y3 ) @ ( Y0 @ Y2 ) ) ) ) )
@ sK0
@ sK2 ) ),
inference(definition_unfolding,[],[f37,f36]) ).
thf(f46,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK0 @ Y1 ) @ ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK0 @ Y1 ) @ ( sK0 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ ( sK0 @ Y0 ) @ ( sK0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ ( sK0 @ Y0 ) @ ( sK0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( sK2 @ ( sK0 @ X2 ) @ ( sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ ( sK0 @ X2 ) @ ( sK0 @ X1 ) ) )
| ( $false
= ( sK2 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK1 @ Y0 ) @ ( sK1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK1 @ Y0 ) @ ( sK1 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ ( sK1 @ X1 ) @ ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( sK2 @ ( sK1 @ X1 ) @ ( sK1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( sK2 @ ( sK1 @ X1 ) @ ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK2 @ ( sK1 @ X1 ) @ ( sK1 @ X2 ) ) )
| ( $false
= ( sK2 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) @ ( sK1 @ ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f59,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) @ ( sK1 @ ( sK0 @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 @ sK3 )
=> ( sK2 @ ( sK1 @ ( sK0 @ sK3 ) ) @ ( sK1 @ ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 @ sK3 )
=> ( sK2 @ ( sK1 @ ( sK0 @ sK3 ) ) @ ( sK1 @ ( sK0 @ Y0 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( $false
= ( ( sK2 @ sK4 @ sK3 )
=> ( sK2 @ ( sK1 @ ( sK0 @ sK3 ) ) @ ( sK1 @ ( sK0 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
( $false
= ( sK2 @ ( sK1 @ ( sK0 @ sK3 ) ) @ ( sK1 @ ( sK0 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( $true
= ( sK2 @ sK4 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f66,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ ( sK0 @ sK4 ) @ ( sK0 @ sK3 ) ) ) ),
inference(constrained_superposition,[],[f63,f57]) ).
thf(f67,plain,
( $false
= ( sK2 @ ( sK0 @ sK4 ) @ ( sK0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f80,plain,
( ( $true = $false )
| ( $false
= ( sK2 @ sK4 @ sK3 ) ) ),
inference(constrained_superposition,[],[f51,f67]) ).
thf(f81,plain,
( $false
= ( sK2 @ sK4 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f86,plain,
$true = $false,
inference(constrained_superposition,[],[f64,f81]) ).
thf(f87,plain,
$false,
inference(trivial_inequality_removal,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET747^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:40:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.26 % (2673991)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (2674005)dis+10_1_sil=32000:sp=arity:random_seed=3548488899:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (2674005) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2673991-2674005"...
% 0.08/0.26 % (2674003)% WARNING: option uhcvi not known.
% 0.08/0.26 % (2674005)...printing done.
% 0.08/0.26 % (2674005)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (2674005)------------------------------
% 0.08/0.26 % (2674005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2674005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2674005)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2674005)Termination reason: Refutation
% 0.08/0.26 % (2674005)Time elapsed: 0.003 s
% 0.08/0.26 % (2674005)Peak memory usage: 12 MB
% 0.08/0.26 % (2674005)Instructions burned: 8 (million)
% 0.08/0.26 % (2673991)Success in time 0.035 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------