%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET747^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:23:28 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 245 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 426 ( 10 ~; 4 |; 12 &; 344 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 5 con; 0-4 aty)
% ( 26 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 111 ( 66 ^; 36 !; 9 ?; 111 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
sK0: $i > $i > $o ).
thf(func_def_22,type,
sK1: $i > $i ).
thf(func_def_23,type,
sK2: $i > $i ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(f2,axiom,
( ( ^ [X0: $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X0 @ X2 ) ) )
= fun_composition ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_composition) ).
thf(f7,axiom,
( ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X3 ) @ ( X0 @ X2 ) ) ) )
= fun_decreasing ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_decreasing) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X3: $i,X2: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X2 ) @ ( X0 @ X3 ) ) ) )
= fun_increasing ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_increasing) ).
thf(f9,conjecture,
! [X1: $i > $i,X2: $i > $i > $o,X0: $i > $i] :
( ( ( fun_decreasing @ X1 @ X2 )
& ( fun_increasing @ X0 @ X2 ) )
=> ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f10,negated_conjecture,
~ ! [X1: $i > $i,X2: $i > $i > $o,X0: $i > $i] :
( ( ( fun_decreasing @ X1 @ X2 )
& ( fun_increasing @ X0 @ X2 ) )
=> ( fun_decreasing @ ( fun_composition @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ ( X0 @ X3 ) @ ( X0 @ X2 ) ) ) )
= fun_decreasing ),
inference(rectify,[],[f7]) ).
thf(f12,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,[],[f11]) ).
thf(f15,plain,
~ ! [X0: $i > $i,X1: $i > $i > $o,X2: $i > $i] :
( ( ( fun_decreasing @ X0 @ X1 )
& ( fun_increasing @ X2 @ X1 ) )
=> ( fun_decreasing @ ( fun_composition @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[],[f10]) ).
thf(f16,plain,
~ ! [X2: $i > $i,X1: $i > $i > $o,X0: $i > $i] :
( ( ( $true
= ( fun_increasing @ X2 @ X1 ) )
& ( $true
= ( fun_decreasing @ X0 @ X1 ) ) )
=> ( $true
= ( fun_decreasing @ ( fun_composition @ X2 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
( ( ^ [X0: $i > $i,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
=> ( X1 @ ( X0 @ X3 ) @ ( X0 @ X2 ) ) ) )
= fun_increasing ),
inference(rectify,[],[f8]) ).
thf(f20,plain,
( fun_increasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f24,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f26,plain,
? [X2: $i > $i,X1: $i > $i > $o,X0: $i > $i] :
( ( $true
!= ( fun_decreasing @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( $true
= ( fun_increasing @ X2 @ X1 ) )
& ( $true
= ( fun_decreasing @ X0 @ X1 ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f27,plain,
? [X1: $i > $i > $o,X2: $i > $i,X0: $i > $i] :
( ( $true
!= ( fun_decreasing @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( $true
= ( fun_decreasing @ X0 @ X1 ) )
& ( $true
= ( fun_increasing @ X2 @ X1 ) ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
? [X0: $i > $i > $o,X1: $i > $i,X2: $i > $i] :
( ( $true
!= ( fun_decreasing @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
& ( $true
= ( fun_decreasing @ X2 @ X0 ) )
& ( $true
= ( fun_increasing @ X1 @ X0 ) ) ),
inference(rectify,[],[f27]) ).
thf(f29,plain,
( ( $true
!= ( fun_decreasing @ ( fun_composition @ sK1 @ sK2 ) @ sK0 ) )
& ( ( fun_decreasing @ sK2 @ sK0 )
= $true )
& ( $true
= ( fun_increasing @ sK1 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f28]) ).
thf(f33,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,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,[],[f12]) ).
thf(f37,plain,
( $true
= ( fun_increasing @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f38,plain,
( ( fun_decreasing @ sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f39,plain,
( $true
!= ( fun_decreasing @ ( fun_composition @ sK1 @ sK2 ) @ sK0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f40,plain,
( fun_increasing
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
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 ) ) ) ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ sK1
@ sK2 )
@ sK0 ) ),
inference(definition_unfolding,[],[f39,f34,f33]) ).
thf(f45,plain,
( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
@ sK2
@ sK0 ) ),
inference(definition_unfolding,[],[f38,f34]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i > $i,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y1 @ ( Y0 @ Y2 ) @ ( Y0 @ Y3 ) ) ) ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[],[f37,f40]) ).
thf(f47,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ ( sK2 @ ( sK1 @ Y0 ) ) @ ( sK2 @ ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f48,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ ( sK2 @ ( sK1 @ Y0 ) ) @ ( sK2 @ ( sK1 @ Y1 ) ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ ( sK2 @ ( sK1 @ sK3 ) ) @ ( sK2 @ ( sK1 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ ( sK2 @ ( sK1 @ sK3 ) ) @ ( sK2 @ ( sK1 @ Y0 ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( $false
= ( ( sK0 @ sK4 @ sK3 )
=> ( sK0 @ ( sK2 @ ( sK1 @ sK3 ) ) @ ( sK2 @ ( sK1 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f52,plain,
( ( sK0 @ ( sK2 @ ( sK1 @ sK3 ) ) @ ( sK2 @ ( sK1 @ sK4 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( $true
= ( sK0 @ sK4 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f51]) ).
thf(f54,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ ( sK2 @ Y0 ) @ ( sK2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ ( sK2 @ Y0 ) @ ( sK2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ ( sK2 @ X1 ) @ ( sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ ( sK2 @ X1 ) @ ( sK2 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ ( sK2 @ X1 ) @ ( sK2 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK2 @ X1 ) @ ( sK2 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ ( sK1 @ Y0 ) @ ( sK1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f61,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ ( sK1 @ Y0 ) @ ( sK1 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ ( sK1 @ X1 ) @ ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ ( sK1 @ X1 ) @ ( sK1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X1 @ X2 )
=> ( sK0 @ ( sK1 @ X1 ) @ ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X1 ) @ ( sK1 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( ( ( sK0 @ ( sK1 @ sK4 ) @ ( sK1 @ sK3 ) )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f59,f52]) ).
thf(f68,plain,
( ( sK0 @ ( sK1 @ sK4 ) @ ( sK1 @ sK3 ) )
= $false ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f70,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK4 @ sK3 ) ) ),
inference(constrained_superposition,[],[f65,f68]) ).
thf(f72,plain,
( $false
= ( sK0 @ sK4 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
$true = $false,
inference(constrained_superposition,[],[f53,f72]) ).
thf(f76,plain,
$false,
inference(trivial_inequality_removal,[],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET747^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n002.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:43:38 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (1300446)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1300461)lrs+10_16_si=on:nwc=1.5:random_seed=2518064352:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1300461) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1300446-1300461"...
% 0.21/0.29 % (1300461)...printing done.
% 0.21/0.29 % (1300461)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (1300461)------------------------------
% 0.21/0.29 % (1300461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1300461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1300461)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1300461)Termination reason: Refutation
% 0.21/0.29 % (1300461)Time elapsed: 0.003 s
% 0.21/0.29 % (1300461)Peak memory usage: 12 MB
% 0.21/0.29 % (1300461)Instructions burned: 7 (million)
% 0.21/0.29 % (1300446)Success in time 0.038 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------