%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM721^1 : 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 : n020.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 08:19:23 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 33 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 272 ( 18 ~; 12 |; 0 &; 236 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 64 ( 32 ^; 32 !; 0 ?; 64 :)
% 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,
u: nat ).
thf(func_def_4,type,
some: ( nat > $o ) > $o ).
thf(func_def_5,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_7,type,
ts: nat > nat > nat ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f3,axiom,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X3: nat] : ( diffprop @ X0 @ X1 @ X3 ) )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X3 @ X4 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34) ).
thf(f4,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34a) ).
thf(f5,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( some
@ ^ [X0: nat] : ( diffprop @ y @ x @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X0 @ X1 @ X4 ) )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X2 @ X3 @ X5 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ X6 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) )
=> ( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X3 @ Y0 ) ) )
=> ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X3 @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f16,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X3 @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( some
@ ^ [Y0: nat] : ( diffprop @ y @ x @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X3 @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) @ Y0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
( $true
!= ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f24,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ X2 @ X3 ) ) )
| ( $true
= ( some @ ( diffprop @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) ) ) )
| ( $true
!= ( some @ ( diffprop @ X0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f25,plain,
( $true
= ( some @ ( diffprop @ u @ z ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f26,plain,
( $true
= ( some @ ( diffprop @ y @ x ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f40,plain,
! [X0: nat,X1: nat] :
( ( $true != $true )
| ( $true
= ( some @ ( diffprop @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) ) ) )
| ( $true
!= ( some @ ( diffprop @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f24,f25]) ).
thf(f44,plain,
! [X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ X0 @ X1 ) ) )
| ( $true
= ( some @ ( diffprop @ ( ts @ X0 @ u ) @ ( ts @ X1 @ z ) ) ) ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f61,plain,
( ( $true != $true )
| ( $true
= ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ) ),
inference(constrained_superposition,[],[f44,f26]) ).
thf(f62,plain,
( $true
= ( some @ ( diffprop @ ( ts @ y @ u ) @ ( ts @ x @ z ) ) ) ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f66,plain,
$false,
inference(forward_subsumption_resolution,[],[f62,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM721^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 12:46:04 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.25 % (997818)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (997826)dis+10_1_sil=32000:sp=arity:random_seed=2298322992:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (997826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-997818-997826"...
% 0.08/0.25 % (997826)...printing done.
% 0.08/0.25 % (997824)% WARNING: option uhcvi not known.
% 0.08/0.25 % (997826)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (997826)------------------------------
% 0.08/0.25 % (997826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (997826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (997826)CaDiCaL version: 2.1.3
% 0.08/0.25 % (997826)Termination reason: Refutation
% 0.08/0.25 % (997826)Time elapsed: 0.002 s
% 0.08/0.25 % (997826)Peak memory usage: 12 MB
% 0.08/0.25 % (997826)Instructions burned: 6 (million)
% 0.08/0.25 % (997818)Success in time 0.031 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------